That didn't do it either, I'm afraid.
I came up with a plan, I replaced dkim.php content with phpinfo() to find which configuration file is used. This one is the correct .ini file:
/usr/local/cwp/php71/php.ini
And I have already set it at 256M as I need it to be. So I assume, there is some service I missed and didn't restart. So far, I have restarted cwpsrv and cwp-phpfpm but to no avail.
Unfortunately, this being a production server with multiple clients on it, I cannot reboot the whole system and be done with it.
P.S.: Why such an old PHP version for CWP? Apparently it runs on 7.0.32
Edit: Also phpinfo report 128M as well, so it certainly hasn't updated the values.