The answer from Spike here was very nearly exactly what we needed. The only hurdle is how to have the backup run on one server and the restore run on another through linked server all in one script? It must be a script that can be turned into a stored procedure that's fed only source and destination DB names.
Does it present a problem that the source server is SQL Server Express 2012 whereas the destination is the full version?
It has to be a script that can run against any DB by just changing the DB name and logical names. It's for a process that's need to run very regularly and fully automatically against a different DB each time.
Also, why wouldn't be better to just detach, copy the mdf and ldf, then re-attach?