Got it! Pages that you don’t want to switch put a comment in their template: <!-- donotswitch -->
Other pages that don’t use that template can still switch back and forth, even to that template and back, but a page with that template assigned to it originally won’t switch. Just took adding another IF condition to the template switcher plugin!
if(!strstr($modx->documentContent, "donotswitch")) {
Now I need to set it up to maintain the user’s choice across pages, except for those with templates that can’t be changed.