There should be a separate gate, that allows for a vote after a player clicked the button to go further down (or after the timeout of said button). The vote would be to choose from 4 or 5 random options. The pool of options would include all stratum themes, but just 5 of them are displayed for a choice. All players in a party would get the same choices. The next map would have the theme, that got the most votes. If everyone voted for a different theme, the theme would be random like an anti mineral disruption (i.e. one of Graveyard, Treasure Vault and some other map). There would be no bosses in this gate. This gate would not lead to the core, but end at an underground sea or something like that. The Gate Map for this gate would be empty, but the already completed levels would show up.
The background story could be, that the knights found a part of the Clockworks, not yet explored. This part is defective and does not spin properly. Before they can use the elevators, the knights patch up the mechanics of the giant cogwheels and can therefore slightly influence the direction or speed a tier spins. During repair they can peek to the next levels near them and thus choose what way to go. ... but they need to work together to some degree, or they end up spinning it to a path they didn't want to take.
Next Map Vote Gate
Theres significant variety within a single theme, and several of the special levels span 2 or more themes. I would say keep the choices to no more then 4. Knowing people, they'll pick a monster theme if possible, and will avidly avoid undead and fiend levels... with only 4 choices, at some point they'll have to choose between an unwanted monster theme, or a taking a chance with a status theme.
I think there will even be parties who try to get as many Candlestick as they can. There are actually some people who love those. I would like them, too, but all the noobs die in Candlesuck and eventually leave me alone :( I hate playing solo.
However, when you get the following themes from the pool as random choices, there is actually a chance that you get a Candlestick Keep, no matter what you choose: Fire, Freeze, Poison, Shock, Undead.
You could avoid all Graveyards, when all party members manage to never vote for completely different things, because AFAIK Graveyards require an anti mineral disruption and in my original suggestion this is solved like that. So you could agree for voting priorities and as long as people obey them, they won't get Graveyards (or get more chances for Graveyards if that would have been their intention). That would be them working together really good to make the Clockworks move more like they want to in the suggestion for a background story.
PS: For reference: Gate_construction#Stratum_Themes
Sounds good to me. Love the backstory.
And it does seem like a good idea that you're planning to use themes - that way it's harder to avoid certain maps like Graveyards or Candlestick Keeps...
Just a little thing to consider, though (yes, I know you hate this part). If the themes were based on, say, monster type, you could get everyone to vote against going to deliberately hard levels such as Candlestick Keeps.
Perhaps you might want to stick with the idea of themes, but give a pretty significant (probably 30%) chance that the next level would be chosen irrespective of the theme selected. This way, it's harder to deliberately avoid certain levels.