Beforehands: You can keep everything RNG about the roulette; the champs, the items - after all that's the essence of the game. Now to my suggestion.
e.g.: The thing that bothers me is if you are #4 because you had some bad draw luck and someone already has two Lv3 Assassins and you want to get that Sejuani with spatula to get her Lv2 and counter him, you will of course be able to move earlier in the roulette, to ensure that you, as a player in a worse spot, will have a better opportunity to get the champ you want from the roulette than someone who already has almost all the stuff he needs. If Sejuani happens to rotate away from you in the direction the #1 (dude with assassins) is, he will get the Sejuani, because sometimes you can't catch up in that time. That's the most frustrating thing of all.
At first I thought making the roulette just another tab to select from would be good, but I don't think it would be.
_But_ the thing you could do, is to even out the distance between players and the champions by putting players on the bottom and the roulette on top. The roulette could stay in the circle form or it could be a line. Leaving it as a circle could actually also make your "skill" more important when trying to pick something that's on the backside atm and you have to decide which way to run around to be first.