I am at level 61 and wanted to remove the High Level Enemies mod. So, I uninstall it, rebuild my BASH patch, start the game (in one of the player homes), save, exit, restart that save, sleep 31 days (using a mod to make that easier), make the Immersive Armors script run again (just to be sure), and now I am seeing the occasional headless naked bandit that doesn't animate, but slides around and talks trash. I feel like I am in a Monty Python movie.

It seems to be random bandits that have included Silver Hand bandits, regular bandits, and bandit chiefs.

The High Level Enemies mod has no scripts. I am revisiting a lot of "cleared" places that are now respawned. Some are for the Dawnguard's radiant quests you get to kill vampires and find crossbow schematics.

Any idea why this would occur? Searching finds reports of this from 2012, but I found nothing related to my situation.

Because there is no "clean save" in Skyrim. Scripts are not the only things that get permanently baked into the saves.