In the end, this isn't a perfect process either, especially if people provide addresses via forum PM due to Cloudflare. I've considered building software to do something like this (more likely it would be in the form of automated address changes), but I'm hesitant to trust any software I write with real sums of money

I won't rule making large changes out, but ultimately there will always be trust needed somewhere. If you're after the highest level of privacy, your privacy model should not rely on needing to trust me to keep your payout addresses private.
You don't need to write any software. Just give us your PGP public key, we send you our addresses over any insecure communication channel (forum post, direct message, anything) and you decrypt them on your machine. Problem solved.
