A non-random ARAM would just be an AM. What a lame name. :P
On a serious note though, you can have your non-random howling abyss games. For years we just played ARAM on SR with our own rules in custom games. Then ARAB evolved when dominion came out. Then finally, they let us use the tutorial map, before eventually making it into the aram map you know now.
If you just want to play all mid, then get up a custom game for it. You could do ADAM (All Draft All Mid) or ABAM (All Blind All Mid). If people want to play it then they'll be there in the custom games.