One solution for enforcing pick order could be to make players pick their champions one by one, not two at once (overall order stays the same).
I like the idea of votekick as an addition to "my" system. But all 4 other players have to vote for a kick, not only 3. Furthermore, 4 man premades will not be allowed to votekick, just because they could votekick as long as they want. This might leave a problem with duos, but in this case, both duos would have to agree that one trolls, and I don't think that happens too much. Last but not least, there could be a limit for kicks to stop exzessive votekicking. 2 per day or something similar.