What you want seems to be the reverse of what EOSPlus is providing.
EOSPlus let’s you use Steam OSS to use EOS. EOS provides crossplay features.
You want to use EOS (EOSPlus) to login to Steam OSS? I don’t see how that would ever work.
For Steam OSS to work you need to own the game on Steam and I don’t know if that is possible or even allowed if the game is bought on EGS.