I’ve been getting conflicting information on which biweekly dungeon series are being permanently shifted to technical dungeons, but the best I can make out from the JP announcement is that the Sengoku and Princess Knight Dragons — known to NA users as War Dragons and Dragon Knights, respectively — are the ones being moved. It’s a good idea to clear these now so you can get the stone again whenever NA gets the update.
To be on the safe side, I decided to just clear all the biweeklies. This ended with me S-ranking the Pirate Dragons with some ROdin cheese. The idea is to nuke every floor, then use RSonia to setup a fairly easy 8+ on-board combo.