After seeing the example photos that were not available when this answer was originally written, there are a few qualifications that should be made regarding the original answer that appears below the line following the newer answer immediately below this explanation.
- It contains accurate information with regard to how the AF system of the 7D and similar AF systems in other cameras operate and how they must be understood to be used effectively.
- The issue that caused the OP's images to be soft near the end are not really addressed in the original answer, but someone else describing their AF issues similarly may in fact be dealing with what is dealt with in the below answer.
- We choose to leave the below answer intact in order to make that information available to those who may find it of use.
- Immediately below is our response based upon examination of the sample images now included in the question.
The first couple of images are reasonably in focus with regard to the intended subject. The third frame includes water in the foreground closer than the previous images and Zone AF, as is often the case, chose to focus on the closest thing it could find. From there the camera totally lost focus and spent the rest of the sequence hunting at distances much shorter than anything in the frame.
All of the images were taken at 270mm and f/6.3 (The EXIF info is viewable at the flickr link in the question). This is the lens' maximum aperture at 270mm which means all AF operations were also performed with an f/6.3 aperture. The 7D's AF system is rated to operate with lenses having an f/5.6 or wider maximum aperture. Many third party lenses, presumably including the Tamron 18-270mm in question, get around this limitation by reporting the maximum aperture of the lens as f/5.6 regardless of the focal length to which the lens is set and the actual maximum aperture at that focal length. But just because the AF system tries to AF doesn't mean it can succeed. As the point of aim of the lens is lowered there is progressively less and less total light in the frame with which the AF system has to work. This is what likely led to the failure of the AF system to focus correctly on anything in the final frames.
The obvious solution is to shoot with a lens having a larger maximum aperture or at least at a focal length that allows a wider maximum aperture, specifically one that is at least f/5.6 or wider. At focal lengths of 169mm and longer the Tamron 18-270mm f/3.5-6.3 is limited to f/6.3. At focal lengths of 168mm and shorter the lens maintains an f/5.6 or wider maximum aperture.
But even then, you still need to practice, Practice, PRACTICE to master the AF system of the 7D!
(Original answer posted before example images were included in the question)
First off, select an AF mode other than Zone AF. In my experience, as well as that of many others, it just doesn't work well when shooting action with the 7D. The camera will likely focus on something, but it probably won't be what you wanted to be in focus. Try either Single-point AF or AF point expansion. Set up your camera so that nudging the little joystick on the back of the 7D can change the manually selected focus point on the fly without taking your eye from the viewfinder and use it to track your subject in the frame. This will take lots of practice!
Once you learn to use Single-point AF this way you can select Spot AF to reduce the size of the coverage area for each focus point. This allows you to tell the camera with even greater precision what you want it to focus on, but it also requires greater precision on your part in placing the coverage area over your target. (Note that Single-point AF works better with some lenses and lighting conditions than others. Since this answer was written I've chosen to use it less unless I really need to thread a needle between two things in the frame at other distances than the intended subject.) This will take lots of practice!
Next, learn as much as you can about how the 7D AF system works. Most other DSLRs with a large number of focus points work similarly. The thing you have to remember is that the areas of sensitivity for each focus point are larger than the representation of those points in the viewfinder. This is especially true when using Zone AF. The camera will focus on the area of highest contrast within the entire area of sensitivity. This will not necessarily be the area directly behind the little square you see in the viewfinder. For an in-depth article concerning this issue, please read Andre's blog.
If there is an area of higher contrast in the active focus area, it is what the camera will attempt to focus on even though that area is not directly underneath the indicated focus point. Learning to see beyond each square in the viewfinder and understanding the actual full areas that are active for each point (hint: they're not all the same) and in various focus modes (hint: they're not all the same) is critical for using the AF system of the 7D to its full potential! This will take lots of practice!
Below is a map of the 7D focus system.
The diagram at the top shows the points as they appear in your viewfinder, with identifying numbers added to the left of each point. The middle left chart shows which areas of the focus array at middle right apply to each focus point (please note that the light falling on the focus array is directed by a set of micro-lenses when the light enters the focus array, so the physical arrangement of the points does not directly correspond to a specific point in the viewfinder). The vertical elements for point 1 are a5 and b5. The horizontal elements for point 1 are a2 and b2. The diagram at the bottom shows the actual areas of sensitivity for each of the much smaller points displayed in the viewfinder. When you have the far left point selected (point 1 in the top diagram), the area of sensitivity includes everything in the horizontal and vertical blue rectangles that pass over that point. Notice that the horizontal line for point 1 is shared with point 3 and the area of sensitivity for point 1 extends completely to point 3! Also notice that all of the area of horizontal sensitivity is directly over or to the right of point 1, there is no horizontal sensitivity extending to the left beyond the viewfinder square for point 1. As far as the vertical middle line (points 8-12) goes, it should be clear that (especially when you are in Zone AF) the entirety of lines a14/b14 can be active!
In order to fully harness the 7D's AF system, you need to know the shape and coverage of each AF point! This will take lots of practice!
The Canon 7D is not unique in the way multiple focus points share parts of the same lines on an AF array. Most of the pro grade bodies and many of the pro-sumer and advanced enthusiast cameras that use an ever increasing number of focus points do the same thing. Learning to harness and use these advanced focus systems, compared to the more rudimentary ones used in entry level DSLRs, is as large a step as learning the ins and outs of the metering systems and exposure options on a DSLR compared to a point and shoot. This will take lots of practice!
If you have done everything suggested above (Learned the ins and outs of the 7D AF system and practiced, Practiced, PRACTICED) and are still experiencing a high rate of poor AF performance you might consider using the 7D's AF Micro Adjustment feature. If your focus most often misses in front of your target your camera/lens combination is front-focusing. If your camera/lens combination most often misses behind your target they are back-focusing. Please see Do the issues with sharpness I am seeing require AF fine-tuning? for more. Also What is the best way to micro-adjust a camera body to a particular lens? and Which offers better results: FoCal or LensAlign Pro? If your camera/lens combination misses focus about equally in front of and behind your target, then you may have found the limits of that camera/lens combination's AF performance. For more please see this blog entry from Roger Cicala of lensrentals.com.
Beyond that, one must realize no AF system is perfect. There will be shot-to shot variation even when the camera is pointed at the same stationary target. Some camera/lens combinations have more variation, some camera/lens combinations have less. Roger Cicala, founder and CEO of lensrentals.com and generally recognized all-around lens guru addresses this issue in this blog post. As Roger observes, your 7D probably can't take advantage of the increased precision of newer Canon lenses that measure how far the lens' focus element actually moves when focusing the way the 1D X, 5D Mark III, and 7D Mark II can. And the EF 300mm f/4 L IS that you are considering was introduced in 1997, so it doesn't have the ability to do that even with the latest bodies. You need both one of the higher precision bodies and a newer lens (say post 2010 when the EF 70-200mm f/2.8 L IS II was introduced) to get the benefit of what Roger has observed. Having said that, a prime Super Telephoto lens such as the 300mm f/4 would be expected to significantly outperform a wide ratio zoom lens such as your 18-270 in terms of optical performance and should allow more accurate focusing due to the wider maximum aperture. With regard to the other lens you are considering, the EF 70-200mm f/2.8 L IS introduced in 1995, the superior optical and focusing performance of the EF 70-200mm f/2.8 L IS II is well documented. Combining that lens with a 2X extender, however, does reduce both the focus speed and the overall optical quality of the lens.