Ooh, this is an interesting one! Because, as everyone noted, most Quirk drains at least try to boost another opposed Quirk, the best way to do this is probably to try and consolidate all your points into a single Quirk that you can then find an infinite drain for.
The Ambition mirrors at the Carnival require only [Quirk] 1 in order to drain it, and do not give any offsets, so those are going to be our best bets for the final drain. Depending on your Ambition, this means we’re going to try to consolidate either Hedonist (Heart’s Desire), Subtle (Light Fingers), Ruthless (Nemesis), or Melancholy (Bag a Legend). You’ll take some stat damage in the process, especially during the last few points when your odds of success drop to 30%, but stats are easy to get back without re-gaining quirks.
As it turns out, those four quirks are completely fungible for our purposes, along with Steadfast, between the cards "The vigilant gentlemen in blue" (Suspicion 5), "Weather at last", and "Bringing the revolution" (Plotting Against the Masters 1), which allow you to trade quirks in an infinite loop of Subtle to Steadfast ("Let destiny take its course" on Vigilant Gentlemen) to Ruthless to Melancholy ("Don’t ask me" and "Follow your conscience" on Revolution) then either back to Subtle ("An opportunity!") or infinitely back-and-forth between Melancholy and Hedonist ("So much has been lost" and "Well, those clouds are quite pretty"). If we can convert our quirks to any one of those, we can ultimately zero them, regardless of Ambition, by playing those cards enough and then taking our business to the carnival mirrors! So the question is how to get Austere, Forceful, Daring, Magnanimous, and Heartless into this vicious cycle.
Since Forceful and Austere are the standard opposed quirks for Subtle and Hedonist, it’s pretty easy to get them involved. Personally I recommend "Keep it bloodless" while Doing Business in Wilmot’s End for the former, and "Buy[ing] drinks for writers" on the Bohemians card for the latter; you may have better Austere to Hedonist options available depending on whether you have, for instance, gotten kicked out of Court.
As it turns out, Daring is remarkably hard to lose! The only repeatable action I can find that lowers it is accepting "surprising evenings" from a player you’re dating, so you’ll need to have your alt date yourself or someone else who can afford to spend Free Evenings on it. I would also recommend taking advantage of the Noman, if you can boost your Daring up enough to use it again, to lessen the requirement.
That leaves Heartless and Magnanimous. Fortunately, we’ve got a card that can do both of those trades for us: purchase a Winsome Dispossessed Orphan and some laudanum, and when he finds the stuff, "Give him a chance to mend his ways" will convert Heartless to Magnanimous, and "Accuse him outright" will turn that Magnanimous into Ruthless.
I hope this helps! Researching all that was a fun and unusual diversion from my normal minmaxing. (I guess this would be maxminning?) Furthermore, this should enable you to remove any further unwanted quirk points you may accidentally acquire.
edited by Jeremy Avalon on 1/15/2016