Our conversion group calculates the base density at 15 °C. We also need to report the base API gravity at 60 °F. Is this possible?

Yes.
API MPMS Chapter 11.5 2009 provides the calculation logic for such calculations. It replaces the historical tables 3, 21 and 51 of ASTM D1250-80 Volume XI/XII.
This new logic has been implemented in an ABAP function for MQCI conversion groups, which requires a base temperature of either 15 °C or 60 °F. Template MQCI conversion group Q22A provides the configuration example:

MQCI ABAP function /QTYW/MQCI_CALC_TAB3_21_51_NEW needs to be assigned to the model function sequence:

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