Just to let you know, I have successfully been able to use the plugin to prune various branches, including those that don't contain common ancestors.
This goes much easier and faster than using the query separately each time, as I only have to add a list of names (just needing to make sure I select the relevant partners) and run the plugin once to do it all instantly. I just keep a list for myself of the names that need to be on there, and if needed in the future I just add names when various branches get linked to each other perchance.
After that, I just have to use the Prune Descendants Branches Query to remove a few descendants here and there, and done.
All in all, the job now takes no more than 5 minutes or so to complete, which is exactly the kind of solution I was hoping to achieve!
Thank you again for all your help to get to this point, for your plugin, and most of all - for your endless patience with me!