This response was helpful and enabled me to resolve the problem, thank you. In our case, there is no user Login at the server level, because the users are administered by an AD group. The group had no default schema for the Sitefinity database. I tried setting the default schema to dbo, but the result was the same when I tried to create a Search Index (duplicate set of tables with unwanted schema). I also tried manipulating the Owned Schemas at the database level without an effect.
I have switched to using a "service" AD account with dbo default schema and all is working properly. This setup creates problems when developing with Entity Framework (due to cross-AD-domain limitations), but we should be able to switch to our "B" users when undertaking that development, and then back to the service account when manipulating the backend. Many thanks.