With Regards to the three possible Solutions listed:
1. Vote Kick
Pros: Allows players to remove uncooperative or toxic summoners from Champ Select, WITHOUT one of the cooperative players being forced to dodge and incur a dodge penalty OR being forced to play out an entire match with the toxic player.
Cons: Opens up limited possibilities for abuse, potentially kicking people with bad stats or unpopular/unconventional champ picks.
Given that this feature would be for SOLO/DUO queue, and that this feature would require a unanimous vote from 4 players, I believe that abuse could be greatly limited. Given the countless instances of one toxic player ruining champ select and an otherwise solid team comp (from experience) I think that this feature would have a very positive effect on the champ select experience. Negative effects and abuse can be avoided by limiting the consequences to the kicked player. A kicked player is removed from Champ Select and must re-queue, but incurs no time penalty and no LP penalty. Consequently, kicked players don't incur any permanent punishment (limiting collateral damage from unjustified kicks). The player has an immediate opportunity to re-queue, change their attitude, and successfully enter another match. However, they also know that if they continue to be toxic/uncooperative, they will continue to be kicked.
2. WoW Dungeon Finder
Pros: Allows ALL summoners to successfully queue for a particular role or champion class/archetype that they enjoy or are competent at playing. Also helps to automate team composition, reducing the burden of team organization on the players within the champion select lobby.
Cons: Would likely increase queue times, especially for popular roles. (However, would also help to reward players playing less popular roles, such as support, with lower queue times). Would likely require an enforcement of a particular team composition framework or meta-game. Would possibly create a constraint on innovative or nontraditional team compositions or champion selections.
Given that this feature would be for SOLO/DUO queue specifically, I believe that Pros outweigh the Cons significantly. I believe many summoners ( or at least myself) would gladly accept slightly longer queue times (which are pretty darn fast at the moment for most MRRs) if they were guaranteed not only that they could play their favorite role, but that they would be matched with a full team that is more willing to cooperate having also been selected for their preferred role. Additionally, this would reward summoners who queue for the least popular roles be providing lowered queue times to for those positions. As for the enforcement of a predefined team framework or meta-game, I believe this is acceptable given the nature and purpose of solo queue. I believe that solo queue (much like PUGs from WoW or other MMOs) are for players who want to dive in quickly, play a roll they know and love and refine their skills, within a predefined framework. Within the current solo queue environment, the solo top/ solo mid/ jungle/ ADC / Support meta-game is closely followed the vast majority of the time, given that these are match-made teams and there is limited time to organize and communicate. The "Dungeon Finder" would simply support players by making this process more automated. Players who wish to significantly deviate from the meta-game with innovative or non traditional team comps with still have the option to do so in Premade Teams (which is where those occur anyway).
Pros: Separates toxic or uncooperative summoners from those who follow the summoners code. Potentially improves the experience of well behaved summoners.
Cons: Would likely create a vicious cycle, in which toxic summoners become increasingly toxic when exposed to other very toxic players. It would also not be easy to escape from such a terrible place, as it would be difficult to detect summoners who are attempting to reform their behavior or become positive influences, as toxic players are unlikely to use feature such as Honor.
I'm not a fan of this idea. The tribunal already exists to deal with toxic players and punish them fairly. The current focus should be on creating features (like those listed above) that improve ALL player interactions and reduce the source and cause of toxic behavior (frustration, pressure, limitations, etc) Players who continue to be toxic will be dealt with by the Tribunal. Creating a figurative "hell" of toxic players does not seem like a good solution for lasting behavior improvement.