I've encountered a situation where barrel A locks up on gun B and seems tight, but barrel B will not lock up on gun A (too tight). If barrel B is too tight on gun A, that implies that barrel A is a bit loose on gun B.
If you can put the 357 barrel on the 223 receiver as easily as the 223 barrel fits the 357 receiver, then the two guns *should* be a match within normal tolerances.
(but it's still your fault if it blows up in your face)
Mitch.