Hi Emcphail.
I supported LDSD and now LDMS, and if that's just moving the SQL server to another, you are absolutely right for your steps regarding the 2 softwares.
The usual though; when you are restoring the DBs, you normally have created a System Admin account to access to it, then think about deleting this account for the DB Restored, on the new SQL server in SSMS > Database > Security > Users. Then create it again in SSMS > Security > Login and map it with dbo schema of course.
In SQL Configuration manager, don't forget to put the same network settings with TCP from the old server.
For LDSD, just IISreset the application server after changing the DB reference.
Good luck!