A few other experiments I would've performed (or thought about performing, before deciding causing a crash of the world I'm currently inhabiting would be a bad idea...):
Holding onto an item on one table while removing it from the other. Related: Attempting to remove an item from both tables at the same time.
Manipulating an item on one table after its appeared on the other already.
Testing interactions of other kinds of biomass-- flora may get different treatment from fauna, and humans may have additional rules.
Using the table when not in its standard orientation or while in motion (rolling it around on its side, maybe).
Placing the tables face to face. Which is probably more likely to have negative effects than an exponentially growing infinite stack of tables.