don't heroes go in a set order, in terms of their speed?
Nope. Page 7, Hero Turn Order, Paragraph 1 of the rules:
The hero players collectively choose the order in which they take their turns each round.
It would have to go into their backpack.
AFAIK the rules don't cover this. So is this a houserule / interpretation of yours or have you been able to find the actual rules in the rulebook?
I was partially wrong about this.
Page 18, Teasure:
During his turn, a hero may give items to heroes in adjactent spaces at the cost of one movement per token or card given. A hero who recieves an item from another player may immediately equip it, place it in his pack, or drop it.