Has anyone disassembled their grilles for detailing?
I have a feeling that the tabs are just waiting to snap if I touch them….

 

Yes, yes they are.
I haven't removed that inner trim before ('72 supreme and '71 supreme grills are my jam and don't have that trim), but I've messed with the outer trim several times. Those thick pot metal tabs will snap instead of bend back to straight. It seems common to use double sided trim tape, glue, or other shenanigans to reattach the trim.
That inner trim looks like it has very thin metal tabs, so those might survive OK. Just move slow, hold your breath and cross all your toes.

 

Thank you for sharing your thoughts….i appreciate it.
I may just try and leave the trim and grilles together, do the best I can with cleaning up, and see how it looks.
They call it “character” right?

 

Yup! I tell myself "I can always do it again" and, usually, I do. At least 2 or 3 more times.