As you have suggested move the LHR-ZRH out a day and book a separate LHR-EDI-LHR.
Yes there are risks. You could move the ZRH out a day now and book the EDI when you get to the UK, or book the last flight of the day and use the SDC to move the flight to an earlier flight when you get to LHR
I quite often buy a KRK-LHR-<somewhere in the us> with a stopover in London and then book a LHR-GLA-LHR on a separate ticket