Thanks for the replies.
I already told my wife to proceed without me since she's only an FO and doesn't have any options if she waits for me. I would catch up with her somehow at our hotel.
The issue may be that TPA and SRQ aren't considered co-cities even though they're relatively close. I could catch a later flight to TPA and drive to SRQ but that wouldn't fall under SDC rules.
I think I'm going to hedge my bets and change to an earlier flight and hang out at the SkyKlub until my wife gets off work. Having a few adult bevs will allow me to properly transition from business to personal travel mode
BTW, the conditions of carriage don't offer much guidance in this situation either. I do know from Binging my question that interline bookings are totally out.