3 crossroads and 4 gears is enough to draw a deck of 21 cards.
I'm trying to work out the math on this one.
You start with a hand of Crossroads + 3 Estates + 5 other cards (
. Crossroads, draw three, + 3 actions (11). Assume you have another Crossroads, Draw three, 2 actions left (14). Gear, draw 2, stash 2. Gear, draw 2 stash 2 (18). You've now stashed Crossroads/3 Estates for your next turn so that your next turn can be identical, but you've only drawn a total of 18 cards. If you play that third Crossroads to draw to 21 cards, you've broken the chain.
That said, your starting 10 + 3 Crossroads and 4 Gears is 17 cards. You can buy just one treasure (even copper!) along the way, and you should be able to buy a Province a turn, which will never clog because Crossroads will replace any purchased Provinces with other cards.
The question is whether that's faster than Gear BM. Could make an interesting simulation. My guess is that you want a +buy somewhere, because spending three turns overpaying for Crossroads and probably overpaying once or twice for Gears seems like a waste. The +buy better be non-terminal or treasure, though!