I have seen other threads mentioning something similar.
I suggest that you might want to use the Price and Inventory upload files to correct the items on both sites to what you want to use (including zeros).
You might also want to double check the pricing in case any of those are getting replicated as well.
Until they get everything fixed up, treat this as an experiment where you are a guinea pig.
Just take a couple extra steps and assume that things might not work out perfectly.
I have accounts on both sites - before the unified accounts - so don't currently have this problem, but expect that once they get everything all sorted out, it should be have some interesting capabilities.
When I compare what they have for European Unified Account with the European Fulfillment Network and Multi Country Inventory, this could be really cool once it is all in place.