But what if we reduced it to 1-3 days and on top of that, they have to do a bunch of things before they can post, maybe like 1-3 daily log in requirement, Bitcoin address requirement (It doesn't have to be their BTC that they are using, it's like for verification only), Bitcoin message signature (maybe if it can be somehow be checked automatically). It's like email verification but it's Bitcoin address that we are verifying.
For spammers, this will be a very tedious thing to do than finding a clean IP and spamming registration on that IP.
This will give new users 2 options, do that or pay the fee.
Won't do. Some of the new users that I've seen were urgently seeking some technical help with their transactions and would probably won't come back if they're made to wait. It is very easy to circumvent log in requirements or address verification. It is not tedious for them to farm large number of accounts at once.
On the contrary, with every trial of finding a clean IP, they need to solve the annoying captcha, register and see the warning. While they can probably shorten their time by using different IP range per trial, it would still be more tedious than buying a bunch of IPs and automate those tasks that you mentioned.