Credit to Spee for accidentally discovering both of these strats in the test stream.

Die right after giving stone/iron pick to Steve and wait until both the chunks have unloaded and when the mobs would've spawned (I use the audio queue of the pick breaking to know that the mobs have spawned. Could probably respawn earlier but too lazy to check). This causes the game to not spawn the mobs as they're in unloaded chunks.

Armoogeddon gets summoned after the 4th lightning strike. Right before the last strike, make shears and put it into the hand slot so that you're holding it. You have 1-2s before the shears break. You then shear the mooshroom. Shearing too early could softlock the game so be careful!