So, I created a completely new plugin with the various overhauls as masters. I then created the new scripts in this new mod. I loaded it with all the overhaul mods that add sheep in the editor, applied the script, and saved.
In TES4Edit, I can verify that this mod now contains entries for all the sheep creatures and the script is applied. I made sure this new mod loads last.
For some reason, even the simple OnActivate block won't do anything. I have to assume its some technical glitch I've not yet encountered, because I tried putting a simple "I was activated" message in the activate block to test and it simply refuses to work.