EDIT: Turns out, I had forgotten DMARC records, and in a scatterbrained state, of course the first few mails went through when I tested, so I assumed, everything is going well. Testing now seems to indicate Gmail is accepting the automatic mails again - please report if you end up noticing issues.
Gmail has started rejecting mail from my mail server - even though I have definitely set up DKIM and other records properly, and they had been getting accepted there before.
For this reason, please use a different mail provider until further notice, when signing up. As long as volume is manageable, I will try to forward the mail to Gmail addresses by hand myself - but this will always have some delay, and is not guaranteed to continue.
I have started an appeal through their system, after I checked that I indeed should be fulfilling all they need on their checklist for incoming mail.
And, thank you again - a quick check showed I was indeed missing dmarc, and a quick test now has gmail working for the automatic signup mails again. Thanks a bunch, again, you made this a whole lot quicker than if I had searched around myself for a solution!
no problem. i love this kind of troubleshooting