Not sure about DL but some other airlines in ST (say, KLM) limit the free stopover to a list of gateway airport

for KLM this list goes something like BOS, JFK, LGA, EWR, IAH, DTW, ORD, MDW, SEA, SFO, LAX, MEX, ATL, MEM, MIA, HNL, KUL, BKK, NRT, HND, HKG, SIN, NBO, FRA, CDG, ORY, LHR, LGW, STN, AMS, BOM, DEL and MSP.

DL might operate a similar system, and neither EDI or GLA may qualify as gateways, so tough luck. But then again, it never hurts to (call DL and) ask