The Canon EF 70-300mm IS USM "II" would be a very good choice and at $500 is well within your budget.
The previous version of that lens is also very good and still sometimes available new, for a bit less money... around $377 now.
AVOID the EF
75-300mm III.... it simply is not a good lens. It's cheap ($199 new, $55 used), but has poor image quality at the longer focal lengths, uses slow/noisy micro motor focus drive and doesn't have image stabilization.
If you want to save some money, at $299 the EF-S 55-250mm IS STM lens is a
much better choice than the 75-300 III.... better image quality, faster/quieter STM focus drive, helpful image stabilization.... but it has a lot of overlap with your 18-135mm and doesn't add a whole lot of reach.
If you want more reach....
The Canon 100-400mm "II" IS USM is superb but is far more than your budget. The older push/pull zoom version of that lens is also very good and fairly widely available used for a lot less, but still more than your budget.
Sigma and Tamron both are also now offering 100-400mm lenses... both with reasonably fast focus drive and helpful IS... that are much closer to your budget, though still slightly more than you wanted to spend ($700 and, $800 respectively). Between the two, I'd go with the Tamron for an extra $100 because it can optionally be fitted with a tripod mounting ring (sold separately, $129) and I'd want that with any lens that reaches 400mm. The Sigma doesn't have option of fitting a tripod mounting ring. Both these lenses are about a stop slower than the Canon 100-400s. They all require fairly good light... the Tammy and Siggy just need more. But you aren't going to find any "long AND fast" lenses anywhere close to your budget. There's simply no such thing.
EDIT: On a Canon 80D you can still autofocus with a
1.4X on the Canon 100-400 II and, so long as it's a good quality teleconverter, get usable images. A 2X teleconverter on that lens WILL NOT be able to autofocus on any of the Canon DSLRs, 80D included. It would be manual focus only and at effective f/11 aperture that will be difficult due to a very dim viewfinder. I imagine a 1.4X could be used on the Tamron and Sigma 100-400s, too... but I suspect the image quality would take a big hit. Neither of those lenses have as good image quality or use fluorite the way the Canon does. That's part of the reason the Tammy and Siggy are far less expensive than the Canon.
Besides, I have used the Canon 100-400mm II a lot for two years and still haven't needed to add a 1.4X teleconverter to it! (And I have one available.)
The $650 Tamron 18-400mm is pretty good for what it is... a "do it all" zoom. The widest ranging one anyone has ever made, in fact. But, don't kid yourself. Both your 18-135mm and any of the 70-300 or 100-400 mentioned above offer higher performance and will have better image quality. For example, the 18-400mm quickly drops down to f/5.6 at about 80mm and f/6.3 at 117mm and longer. In comparison, the Canon 100-400 II is f4.5 or f/5 through 311mm and f/5.6 the rest of the way. Although not as bright as the Canon 100-400 II, both the Sigma and Tamron 100-400s also maintain larger apertures much deeper into their focal length range than the Tamron 18-400mm does.
All the "do it all" zooms compromise in a lot of ways. There is a good, thorough review of it (and all the other lenses mentioned here) at
https://www.the-digital-picture.com/Reviews/Tamron-18-400mm-f-3.5-6.3-Di-II-VC-HLD-Lens.aspx If you are traveling and in situations where you can't change lenses... or just lazy and don't care about performance or high image quality... a "do it all" like the 18-400mm might be perfect. Some people love it.