Originally Posted by
Homebrew01
...but most retro bikes don't have an adjusting cable stop.
Actually, many retro RDs did, perhaps most. Depending on the setup you may be able to install one even if the RD didn't. But the problem can be real; we try to have cables which don't go too slack with the lever all the way forward but sometimes we leave them just a bit tight. But that doesn't necessarily explain why the big ring is problematic and the small ring isn't.
+1 on the benefit of a new chain.