Start with UGC banlist.
Every player picks up to one item not on the banlist to ban.
Then, from the list of items banned by every player + the UGC banlist, every player gets one "lock" and one "save." They can lock up to one item to prevent it from being saved and they can save up to one item to take it off the banlist if they want to.
Each round of picking would take up to 2 minutes on average probably, and there are going to be a lot of people who just skip to get into the game faster, so I'd estimate this would take around 5 minutes. If we let people start picking bans while they're waiting for players (don't show the results until all 18 are present and have picked though), then that can speed it up even more.
After the game, a window pops up asking if the player thought they made good choices with their picks and if they thought an item that was allowed had a big impact on the game.
Everyone needs to keep in mind that Valve isn't going to look at the bans and assume the most banned weapons are overpowered. They're going to assume that those are the weapons that people want to see the least. It signifies a need for reworking, not for nerfing. If they ban sandvich everytime, valve sees that a large portion of the community doesn't like the heavy to carry a hp kit. That doesn't necessarily mean it's too strong, it's just not fun to play around.