Meaning I can wiggle the tower back and forth. Should it have that much give?
No, mine has no give at all. It is rock-solid. Your problem seems to be a somewhat common issues with resin printers from China (screws that hold the z-arm getting loose during a long transport). You have to tighten the relevant screws. I don't know where those are on the LD-002H. Other forums suggets to open a door on the back to get access but mine doesn't have one. They might mean a door on the bottom. Didn't check, dont' have this problem.