Why not charge Tor and VPN users a small bitcoin fee to log in? Most of those users would probably rather pay a fee than use cloudflare. They already have to pay a fee to register.
Paying a small fee to register and paying a fee every time you want to log in are two very different things (not to mention the latter being ridiculous and not sure why we should punish all legitimate tor users).
Well how about asking tor users to sign a message from the bitcoin address they registered with instead?
Each time they log in they could be given a unique code and asked to sign a message containing it. That wouldn't cost them anything, and signing a message would be faster than going through endless cloudflare captchas.