Hey Mark:
From my limited knowledge I believe the STC is typically assigned to the "airplane". While practically this isn't an issue (heck, the plane doesn't care) it may prove to be a regulatory challenge & problematic for a A&P IA sign-off as well as a future sale if an STC re-assignment isn't sought.
Take a good look at the paperwork and if it needs to be re-assigned a quick call to Del Air HQ might be in-order to ensure they'll sign it over in a timely fashion and verify what will be charged for that re-assignment.
Good luck ....
