It appeared that normally they not really check if it matches, but this time given the transfer amount they did. And it just so happened that the signature they had scanned in their system was the first one I ever made as a kid (30yrs ago) when I opened the account.
Finally after many retries they turned the monitor to show me the expected signature and let me practice it on a piece of paper, so it would pass some other approval stage.
With a 200 yard line waiting behind me, sweating profusely, I finally managed to reproduce something. The sale went through, luckily, and immediately after I ditched that bank account.