I think you will find that many of the older and cheaper 70-300mm lenses from Tamron and Sigma will not be that much, if any, of an improvement over your Tamron 18-400mm, either optically or in terms of AF speed and performance. Some, particularly the EF 75-300mm f/4-5.6 III, could be worse. I've still got a Sigma 70-300mm f/4-5.6 APO DG from the mid-1990s. It was adequate for 4x6, 5x7, or even 8x10 prints made from 35mm film but not so much so for the way we tend to view high megapixel digital images. Not to mention that there are firmware issues when using it with a digital EOS camera. You're very likely to run into firmware issues with third party lenses that are much older than your 80D.
The Canon EF 70-300mm f/4-5.6 IS and EF 70-300mm f/4-5.6 IS II both show noticeable improvement over the Tamron 18-400mm at 300mm, even with the Canons wide open at f/5.6 compared to the Tamron already at f/6.3 wide open.
The two 100-400mm f/4.5-5.6 L IS lenses from Canon are better optical performers than anything in the same range from Sigma or Tamron. Here is how the two Canons on the left and center compare to the Sigma 120-400mm f/4.5-5.6 on the right at 400mm:
Notice that the older Canon 100-400 is about as sharp in the center of the frame as the newer version, but the newer lens holds that performance all the way to the edges and corners, while the older one dies not. How you tend to shoot and frame will determine how much of a difference that will make for you.
Are there other options which I'm not taking in account?
Yes. There are a few others to consider.
In the bargain department there are the APS-C only EF-S 55-250mm series. The EF-S 55-250mm f/4-5.6 IS STM holds its own against the more expensive (FF) 70-300mm f/4-5.6 IS II. The older EF-S 55-250mm f/4-5.6 IS II is a step below and more at the top of the class of the cheaper 70-300mm zooms from Tamron and Sigma.
Though not as long, for image quality and (most of the time) AF speed and performance, the 70-200mm lenses from third party makers as well as Canon are another cut above any of the lenses you have listed. There's not as much difference when used on APS-C cameras, but all of these lenses can also be used on FF cameras, and that is where the differences become noticeable. 70-200mm f/2.8 lenses are near indispensable workhorses for sports shooters who need the f/2.8 aperture when shooting under lights at night or indoors. In brighter daylight an f/4 maximum aperture will usually suffice. The Canon EF 70-200mm f/4 L (the oldest non-IS version) can be surprisingly affordable. Used prices for the EF 70-200mm f/4 L IS have also loosened up a bit since the introduction of the EF 70-200mm f/4 L IS II, which is a significantly better lens.
If you need good optical performance and can live with slower AF, the oldest Tamron 70-200mm f/2.8 (Tamron SP AF 70-200mm f/2.8 Di LD (IF) Macro (Model A001)) can be had for a good bargain. For great optical performance the newer Tamron SP 70-200mm f/2.8 Di VC USD (model A009) and SP 70-200mm F/2.8 Di VC USD G2 (Model A025) are in the same class optically as the Canon 70-200/2.8 L IS II/III. The current Sigma 70-200/2.8 lenses seem to be just a tad below them.
Most of the Canon 70-200mm L lenses take 1.4X Canon extenders very well with not much loss in terms of IQ, though AF will be a bit slower. A 1.4X extender makes a 70-200mm f/2.8 into a 112-320mm f/4, and a 70-200mm f/4 into a 112-320mm f/5.6. The only ones I would consider shooting sports with using a 2X extender, which makes a 70-200mm f/2.8 into a 140-400mm f/5.6, would be the EF 70-200mm f/2.8 L IS II / III.
