Very good discovery, like all of you here have been trying to discover the root with FB & Shop helpdesks with the same frustration as you guys.
For me one FB agent told that the reason is URLs not pointing to correct location in my Shopify and suggesting also about the domain verification which was correct and working in FB shopping experience just fine.
Waiting for your valuable update if you can move to private domain now or there needs to be support case opened for the Shop-IG integration.