those 70's mirrored gold vein squares  

I've always kind of liked tho...
I've always kind of liked those gold-veined mirrored walls and not for any retro/throwback/kitschy reasons. They're classy in a way. They're real heyday was actually around '66 '67, so to me, they don't look overly 70's -- which connotes shag Dupont carpet woodgrain toilet seats. I'd leave em.

I'd leave em too. Don't try...
I'd leave em too. Don't try too hard and just learn to love it in its own right,

They're
icky.
How about a film that could be removed when you leave ? White would let just a little of the effect through, while "editing" it to an acceptable degree.
Glass is one of the easiest surfaces to clean thoroughly; I'm sure there is an adhesive film that would be completely harmless to the mirror tiles. Start with a glass company. . .

Upholstered walls
You can put stiocky backed velcro on the mirrors and the floor and ceiling levels and then on fabric and removeably upholster the walls. Saw it done at a friend's place in her basement it looked pretty good, actually. She also anchored the fabric vertically with velcro at the seams. She used a bulap-linely kind of fabric and some light-weight fiber batting to give the fabric a bit of loft from the wall. It really looked pretty decent.

spelling disasters...
that was 'sticky-backed' and 'burlap-linen-y'