the issue is that it is a separate connection that is being spawned.   Can the work be done using the process of the trigger, because nothing would be locked to...

My guess is that the diagram lives with the database, and even if you could figure out how to move it by manipulating the system tables, you wouldn't want to...

Very true. 

I had a physics teacher that loved to ask suddenly "is that fast?"  or "is that small?" after lecturing on a speed of a beam or size of...

You must be sysadmin to create dbo tables, and then it does it automatically.

db_owner is not the same as dbo.