I've successfully used Halfords acrylic black satin finish spray paint on various pistols and rifles, but never tried the gloss alternative, although I see no reason why it shouldn't work just as well.
I've also never had to refinish any of my 600's, but from the sound of it, your 'restored' 600 didn't have a very good finish applied.
I think your idea of stripping, keying then refinishing is possibly the best way to go, although I am sure there will be others on here who may have successfully used alternative methods to refinish their 600's.
Cerakote seems to be a modern popular method of refinishing, although should be professionally applied, but not having had any experience of it, I would suggest you contact RichardH on this BBS who has his own refinishing business.