I'm curious to know what, in particular, is prompting you to ask for Off-Off-Broadway specifically.
Despite some of the "rules" that people often cite, the line between Off-Broadway and Off-Off-Broadway can be a little bit blurry and arbitrary. This is mainly because "Off-Off-Broadway" isn't a real designation - it's just a catch-all term for "everything else in NYC." Which is a really wide net, and hard to keep track of.
And even though Off-Broadway IS a real designation, it can be still be kind of arbitrary. There are some shows that call themselves "Off-Broadway" (including some on your list) that are super low-budget, non-union, and/or off the beaten track. So they might as well be off-off-Broadway for all intents and purposes.
And likewise, there are shows put on by major, venerated companies, with big budgets, and even high-profile artists - and yet, if they don't TECHNICALLY operate under an Off-Broadway contract, they won't always be listed as an "official" Off-Broadway show on places like IOBDB.
So, unless you have a really specific reason for seeking out shows that aren't operating under an Off-Broadway contract, my advice is just to find out about as many shows as possible, and just see what interests you.
As for finding out about as many shows as possible, my advice would be to utilize Show-Score, maybe TodayTix, and also keep your eye on the press releases on the All That Chat message board
