Heh, answering my own questions from the OP here: Instruct fails when attempting to force the use of any rampage (Thrash), charge (Dig), or recharge (Hyper Beam) move. Sadly, the Charge -> double Electric attack trick I thought of doesn't actually work out that way; only the first one has its power doubled.
Edit: Also, I noticed this a while ago but I now see it hasn't been posted in this thread: Instruct causes the move used to use another PP.
Stomping Tantrum gets its power doubled after every "But it failed!" scenario I've tested so far, which includes both types of move failure (those that activate Protean and those that don't). Launching moves into immunities and no target also triggers the boost, but launching moves into Protect does not.