All Random All Mid (ARAM) is a custom game that hundreds of people enjoy, and the ARAM community would be greatly appreciative if you would make a custom SR map focused just on this game.
By this I mean tweak your SR map with just a few modifications, and make it a playable custom game. (A game you can queue up for, rather than have to set up a game) There are numerous benefits that could come from a game set up solely for ARAM.
If I were to make a game mode out of SR specifically for ARAM's I would do the following:
1. Disable creep waves that travel to the bottom and top lanes. This would eliminate the extra 150 gold teams receive from turrets that are killed by "OP Minion waves".
2. Make all turrets, top and bottom, invulnerable. Same benefit as number 1.
3. Remove the jungle minions. Less tempting to cheaters, etc.
4. Disable the back button, this would further mitigate any cheating that may occur.
5. Disable the fog of war for the entire jungle. It would be easy to know exactly who is cheating, and who isn't.
6. This is just a pipe dream, but somehow make it so the fountain would attack anyone who left mid lane, and clearly make the boundaries visible.
7. Implement a "Vote Kick" command that would require 2/3rds majority needed to kick a champion that is intentionally cheating, or feeding the enemy team.
I am by no means a programmer, but I imagine points 1-5 would not be terribly difficult to implement into a custom ARAM game, I imagine points 6 and 7 would take some work.
All of these points make cheating impossible except for the one aspect of actually running your champion back to base manually. At this point I hope the enemy team would have the integrity to step up, and call out the cheater on their team, and start the vote kick. The great thing about ARAM's is you can still snatch victory with only a team of 4. If the offender is kicked out of the game early, your team will out-level the other team, as well as be able to farm more efficiently being shorthanded.
I will now yield to the community for any suggestions, or to cover anything I may have missed.
The ball is in your court Riot, I know you will make your community happy.