Is there any way to set up the change tracking tables - the ones that are created with a suffix "-CT" in a separate database?

We have a high transaction environment and the _CT tables can grow to enormously large tables and if they are in the same database, the backup sizes become huge.

Any solution that we can think of?

We can have these tables in a separate file groups, but we take transaction log backups for log shipping and we also need to take full database backups.