Okay, long story short, there's a mechanic in puzzle games called Entry Delay. It's a brief pause before a piece is spawned, so the player has time to prepare.
Xross Dreams has an entry delay of 7 frames. This value was intended to be an option, along with Delayed Auto Shift and a few other extremely finicky high-level puzzle gamer sensitivity mechanics.
Anyway, ED was being decremented once per frame, which is perfect. The problem is that online play updates each player's boards and physics separately each frame. This was causing a 0-7 frame desync depending on the internet connection and relative processor speeds.
Now, in online modes, Entry Delay is calculated individually alongside other board physics at the end of each player's individual frame calculations.
There were some other changes, but that's the most important one. Let me know if online play desyncs less, and after I take the rest of this evening off I'll get to handling some of the stability problems.
Thank you for your patience.