John's suggestion:
In an ideal world, we should first place this thread poorly, ask for more cores, and re-place it when more cores become available.
When a core arrives, reconsider everything. Ask Arachne to tell you about all the threads that have a particular class. Then we find all the ones that are marked exclusive and see "are they in fact exclusive?"
If not, then fix it.
This mechanism should fix other races with incorrectly placed threads.