You can attach transmogs to off type pieces by applying the mog to an apprpriate chest armor type, saving the full outfit as a template within the mog interface, and then applying that outfit template to your entire set after you switch your chest back to leather.
[doublepost=1631298714,1631296797][/doublepost]Sounds like you are doing exactly what you should. It's possible they fixed it, maybe when they added the option to mog shoulders individually it got patched.
I used this exact method to mog the Master Engineer's goggles on my hunter in late BFA a few months before pre patch.
worked as of BFA, but I have not had a need to test it since the squish. Unfortunate if so.