Visited Scotland in 2021 and decided to fly into London and then connect to BA on a separate ticket. It made more sense with the covid restrictions at the time and didn't take us as far out of the way as Frankfurt, an airport I loathe. The nonstop UA flight was not operating at the time.

I bought a ticket in business on BA to get access to the lounge at LHR, and they served a three course meal on the short flight that was better than UA transcon first meals.

Anyway, if I were you I would take the nonstop IAD-EDI flight and avoid connections all together. Why not do that? Yes, it's on a 752, but it's such a short flight anyway. And even if you're thinking the seat will be better on a widebody, connecting through FRA, you're going to add hours of connecting time (including stress and one or two of those 100 mile bus rides they love at that airport) and sitting in an economy sized seat on the hop to EDI. Connecting in FRA will add probably five hours to what would otherwise be a seven hour trip.