Straight up, I agree with TeamSpeed's comment above. With Tamron's latest issues, I'd suggest taking your lens to a retail outlet (BestBuy?) and mounting the lens on an 80D. If you get auto-focus, you're good.
There are other ways to improve your high-ISO results. Are you shooting raw, exposing to the right (ETTR), and processing your files for best results? Buying an 80D will surely help any noise problem, for about $900. None of the aforementioned methods cost anything at all. If you expose and process your shots with care, you should not see much noise in photos from the 650D at ISO 6400.
I understand that you are happy with your lens. All well and good. Have you tried a fast prime for whatever focal lengths you need high-ISO help with? I doubt you are shooting much high-ISO work at 300mm. If you are, faster glass is prohibitively expensive (300 f/4 IS ~$1000, used). If you need help at shorter focal lengths, like 35 to 85mm, you can get a fast prime for about $300, used. The EF 50mm f/1.8 STM is an excellent lens and goes for about $90.
I am just guessing here, but your current lens is about f/4.5 at 50mm. The 50 1.8 is 2-2/3 stops faster. That translates into dropping your ISO from 6400 to 1000 to get the same shot. Of course, there are other considerations like DOF, supplemental lighting, and so on.
The 80D will net you less noisy photos. Spending $900 on a new camera isn't the only, or even the least expensive, way to get there.