Will I really see photos better enough to warrant the cost?
Honestly: Probably not. Taking better photos has a lot more to do with the knowledge, experience, and creative eye of the photographer than it has to do with the minor differences between reasonably comparable lenses or camera bodies.
Unless you can articulate what it is about your two current lenses that limit your ability to create the photos you wish to create the slightly better optical quality and slightly faster maximum apertures likely won't make any real improvements in your photos. In fact, unless you are aware of the limitations and how to deal with them when using wider apertures you could actually wind up with pictures that are not even as good as you might get with your two current lenses.
The primary advantages of the three "L" lenses you are considering are in the areas of durability and resistance to adverse environmental conditions. Those attributes are critical to working pros who put their gear through the wringer every working day. Yes, they are a little better optically than your current lenses. Their "sweet spots" are larger in terms of the focal lengths and apertures at which they perform at a slightly higher level. But they are much closer to your current lenses in terms of optical performance than they are to the true premium lenses in each category such as the EF 11-24mm f/4 L, EF 24-70mm f/2.8 L II, or the EF 70-200mm f/2.8 L IS II. Even those lenses only make a noticeable difference when used at or nearly at wide open apertures. At f/5.6 or f/8 there's very little real world difference in optical quality.
If you really want to increase the your ability to get shots on your vacation that you can't get with your current lenses, you might consider an ultra-wide angle lens such as the EF-S 10-22mm f/3.5-4.5. But that would only be good if you are interested in capturing wider vistas than you can with your current 15-85.
All those years I wished I had quality L glass... Because, as someone said, a lot is in the eye. I feel I have that. I shoot only in manual mode, and look for those color popping... Sharp scenes I suspect comes with "good glass".
There's nothing "magical" about L glass. For instance, the EF-S 17-55mm f/2.8 IS is better optically from about 24mm and up on a crop sensor than the EF 16-35mm f/2.8 II. It's also nearly the optical equal of the original EF 24-70mm f/2.8 L when the "L" is on a FF body and the 17-55 is on one of the more recent crop bodies. The newer 24-70 is a lot better optically from 24mm all the way to 70mm at every aperture, even the wider apertures, because the newer high resolution cameras revealed the flaws of the older 24-70.
At the f/5.6-f/8-f/11 apertures used for most landscape shooting pretty much every current lens from Canon, Nikon, Sony, Pentax, etc. are very good across the frame assuming they are in proper alignment and designed to have a flat field. There are some very expensive lenses designed for certain uses that leave field curvature uncorrected. That's one of the things that makes the EF 85mm f/1.4 L a portrait lens with such a unique look. Such a lens, even though costing thousands of dollars, is not a suitable lens for most landscape work.
I suspect those color popping sharp scenes have more to do with catching the right quality light at the right angle with a camera mounted on a rock solid tripod. I've known many a landscape photographer to go to the same spot day after day after day until they finally get just the light they want. One day it may be too cloudy. The next day there might be too much, or maybe not enough, moisture or dust in the air. The next day it might be raining. Just because you are standing in the same spot from which an iconic photograph was taken doesn't mean you'll always have the same light, even if you have the same angle of the sun. There's nothing like the light coming from a low angle sun late in the afternoon after a thunderstorm has just passed overhead and the sky is clearing in the west. The light is so saturated and golden you can practically feel its warmth as it bathes everything it falls on in technicolor and makes the world look like a Kodachrome slide. Yet the same spot at the same time of day the day before or the day after may look flat and lifeless under dreary skies.
In the digital age we can "fix" the light in post a lot easier and with a wider latitude than we could in the color darkroom, but we still can't move the sun from one spot in the sky to another.
Here's my suggestion: For the next couple of weeks go out the same time every day with your camera, tripod, and cable release to the most scenic spot in your area. Go when the sun is most favorable for your selected location, probably early morning or late afternoon. Take the best shot you can using the tripod and cable release. If the shutter time is under 1/200 second use mirror lockup as well. On even numbered days use your 15-85 at somewhere between 55-85mm. On odd numbered days use the 55-250 at somewhere between 55-85mm. If you have a 50mm f/1.8 or other prime lens, throw it in the mix as well. At the end of the two weeks edit the best capture of each day and compare the 14 photographs. Let us know what you think of the 14 photos and how each compares to the others.
There's an old saying that's been around a long time: Gear doesn't matter.
That's really only half the story.
The full truth is: Gear doesn't matter - until it does.
When the limits of your gear truly begin to matter to you and where you are in your growth as a photographer you'll know it.
P.S.- The reason the 16-35mm f/4 gets better reviews is because unless you really, really, really need the f/2.8 aperture to shoot moving subjects in low light the f/4 lens is just as good or even better at all apertures above f/4. And it's cheaper to boot.