I already have it set to disallow multiple instances from the settings by the way, so I take it it has to be a bug of some kind.
I'm on the latest public preview build as of this post, is this being looked into on betas? Or has there been attention brought to the issue already, at least?
It's come up a few times though I don't know how common of an issue it might be as I often seem to not get direct reports about issues (aka having to trawl through social media posts) so thank you for taking the time to report it.
If multiple instances are being launched then my first hunch is it might be due to a permissions issue or a form of process isolation which would then prevent the handling that's run on loading to try to find existing wacup instances to fail as that's how that stuff generally behaves afaict. It however doesn't seem to account for how you've described things as seemingly starting all of those instances at the same time instead of it being a gradual cascade from the first to last instance.
My other hunch especially with what you've described about files missing when it is already running could even be due to the processes that have been spawned potentially failing / silent crashing. This might be more likely & from feedback from one tester with the current beta vs issues seen with the preview build seemed to resolve what was a slow / laggy response to start & iirc that was sometimes causing other instances to begin due to the timeout that's in place to deal with hung / failed processes timing out.
One thing you could try out is seeing in Task Manager's details view & sorting by exe name if any werfault instances (windows error reporting handling) are appearing at around the same time as you're triggering trying to get the files into WACUP.
I also could do with knowing what skin you're using & if you're using a modern style skin another thing is to try using a classic skin just to see if the reduced loading overhead of those skins makes any difference or not (I suspect it likely won't & is something else going on).
Final thought for now is if you've got the local library enabled & if so roughly how many items are in it. As going to preferences -> media library & temporarily trying this out with the whole media library disabled might also be useful to rule out some ideas I've got.