I think this is the kind of card that, as written, will give you more rules-headaches than cool moments. I think I know what you're going for here but as written this card really makes for some memory-induced rules difficulties in play.

I'm considering deconstructing this a bit; making an activated ability that turns one equipment into another equipment until end of turn, and a second activated ability to turn one non-equipment, non-creature artifact into another non-equipment, non-creature artifact until end of turn. Wordy, yes, but it's a mythic.

Also, I suspect the cost will drop, as a limited pull probably has very few pieces to mesh with it.

This is broken. Not only does it make all equipments you control give all the bonuses each other would give. In my EDH deck as soon as this landed everything in my deck would be shrouded and indestructible including it. If it said they only shared activated abilities it would be a little better, but it would still make the mana ramp in the deck run wild.

You make a very strong point. It's going to have to require an activation to temporarily "morph" one non-creature artifact or equipment into another.

Is there a way to word it to prevent putting the same aura or equipement into play that was returned to the player's hand? I suppose this is mythic but the most annoying use of the Master Transmuter is that for and tap can make any artifact invulnerable by basically blinking it.

Not only that but could be bonkers with auras or equipement that provide shroud or protection. Can just return said aura / enchantment and put back into play on anything that is being targeted at any time and nullify anything an opponent ever tries to do once a turn.

Dan (Bombshell) and I have been bantering over this one for the better part of the day. I think the point of this card IS shenanigans, though hopefully not outright broken. Annoying is fine, but I feel like it's costed so as not to be backbreaking or abusive. I should ask Okamoto to test a proxy for me...