An Epi case definitely will work. I keep my 3 big headstock 60s-70 TBirds in them.
IMO you're not going to get much lighter than the stock tuners even if you use the special order Hipshot (small) clovers. Maybe try a wider/grippier strap.
I have a late model Gibson USA TBird case: black 'snakeskin' exterior, white interior. Exterior is mint, combination has never been set. Interior has a slightly discolored area. It's big and it's heavy.
I'd entertain offers on it.
Personal opinion, I'd go for an Epi case.