Why don't you add a double effect?
Something like:
"Turn target permanent into a Golden Relic, or turn target creature into a Golden Statue".
This way there is no problem of a creature going into permanent slot.
Also, you need to create a Golden Statue card, something with 0 attack and big HP. And maybe the "vend" ability or something else.
Only thing i don't understand: making something eternal sounds like aether to me, so why you choose time?
Ah, that's one of the problems of letting it affect creatures.
If it could turn creatures into Golden Statues (in some versions of the myth, King Midas did in fact turn his daughter into a statue), then it would take away from the power of Basilisk Blood. It would also be harder to balance, since it would then be a means of both permanent and creature control.
As for its elemental placement, Aether is not about the eternal -- rather, it's about the unyielding (hence the immaterial creatures it has). Time, however, is concerned with controlling the flow of time and becoming eternal. Plus, the Vend ability gives card draw to the owner of the Golden Relic, and drawing extra cards from the deck is an ability that's exclusive to Time.