Well, shortly after I posted I found a solution :-)
On the master database on the Azure SQL Server I ran:
SELECT d.name, d.owner_sid, sl.name
FROM sys.databases AS d
JOIN sys.sql_logins AS sl
ON d.owner_sid = sl.sid;
This did NOT list the database in question as being owned by our admin user. It only listed the databases that were acting normally. In fact, the problematic database wasn't listed at all.
So then I switched to the problematic database and ran:
ALTER AUTHORIZATION ON DATABASE::OurSchemaDbWithTheIssue TO [our-sa]
Running the first query again show what I expected, and the LLGLGen sync wizard can correctly see the database schema I wanted.