So I think I've figured out how you'd go about getting one of those nutty all-vault boards.
First, build up a huge reserve of turns--often enough I'll get to the point where I've gotten my first vault & I've banked about 20 turns.
Someone who could double or triple those banked turns in the early game--who could get 40 or 60 turns--would then be able to play them out as the board filled up with vaults.
At some point, the vaults would start to work in your favor. Sort of. The board would keep rearranging itself until you could make a valid turn. If you had a whole bunch of high-value chests and the board kept jumbling until you could make a valid turn, you'd end up with a board full of vaults.
Really, the trick would be getting enough reserve turns early on, and that's entirely plausible.