I had the same problem. Is a know defect.
"Variant Manager does not support multi-board projects is a known defect: DR/ER #00881041
Reviewed a minimum of 3 times during the normal planning cycles and not selected for inclusion in a release. Closed: Outside Product Roadmap. If you have additional concerns, please contact your Customer Support Representative.
Resolution: Will Not Fix"
The workaround is to put each board in its own project! How fun!