If you frequently play ARAM then surely you noticed that some players will reroll fast without asking others if they want their champ, at least i have faced it alot where i got a boring champ, and someone on my team for some reason rerolled while he had blitz or morgana which i enjoy playing in aram.
I suggest that riot adds a "bucket" somewhat of a graveyard of the rerolled champs on your team that you can pick from, as if you have swapped with that player before he rerolled.
for example, If player 1 got blitz and rerolled , while i got poppy, and i could swap with him but he rerolled fast without asking, then i can pick blitz from the bucket which is the equivalent of first trading then rerolling.
this will also make it easier for all, just reroll no need to ask anyone, and if they wanted what you had then they can pick it up from the bucket.
this is in addition to the current trade function and not instead.