Actually, perhaps I jumped the gun on the threading? The documentation for PopupMenu says that you can use ModalComponentManager::Callback to run the menu asynchronously. I was assuming that this involved threading, but I can’t see any mention of it in the documentation.
I’ve followed the advice on this post and so far everything seems to be running, though unfortunately I haven’t figured out a way to test it properly yet. My main aim here is to ensure that the menu doesn’t interfere with the running of the application in any way. Is an asynchronous menu using ModalComponentManager::Callback sufficient for this?