Headlight, cowl light, radiator shell Stainless Restoration?

[CC-Mo]

A question for restoring these bits to the group.
I could write a book on polishing aluminum but am new to stainless.
My 90 y/o paint has enough character to go around but I'd like my stainless parts to look decent.
They have character that won't polish out fully with metal polish.
Question is, do the restorers use 4000 grit and then polish out?
I've repaired aluminum blemishes this way. 2k, 3k, and then follow up with 4K grit and then metal polish.
Thanks in advance for any pro-tips from those that have been down this road!