I'm trying to make a lever that will basically flip the six of all the mannequins in my mod. Is that possible?

Also, I'm aware of the console command, but I want to do it via scripting.

You could do it, but it'll be a little more involved than you may expect. If you try to do something like the console command, it may end up with 'grey-head bug'... and I don't think there's even a way to do that in Papyrus.

I would recommend creating your custom NPC mannequin (actor baseObject), deck it all out as a mannequin should be (remove extra items, AI, factions, etc; assign proper AI and script). After everything is the way you want it, save it and the plugin. Then you would make a clone of that NPC (r-click, edit, change the edID, save it, reopen it, change the six, resave it). But you THEN need to select the baseObjects of those NPCs then press control-F4 to auto-gen the head meshes and textures (which need to be included with your mod when uploaded). If you don't, you'll get the grey-head bug.

Now in your script, you'd have code which places a new ref of mannequinB, removes any items from mannequinA to mannB's inventory, deletes mannA, and then repositions mannB to the proper spot. This could be done in a messageBox, through a dialog system, a lever onActivate event, or whatever you feel like really.