Some of the United B772s are 36F, 0C, 89Y+ and 223Y (total 348) so one of these might be better suited to EDI-EWR rather than 2 x B752s per day if EDI could accommodate it?
The Delta B763s were able to fit onto one of two stands in the cul-de-sac on the main apron (2 and 4) but these stands are currently too narrow for a B763 with winglets and all of the United B763s are being retrofitted with these. The CO B764s are too long / too wide for the cul-de-sac stands (they have a wider wingspan as well as being longer than a B763).
Possible solutions for the B764 or B772 would be to strengthen the PCNs of the links between taxiway alpha and the SE apron and/or making diagonal stands available on the north-west facing part of the main apron (where BA and BD LHR flights, amongst others, currently park). I'm not sure whether or not it would be feasible to widen stands 2 and/or 4 to accommodate a B763 with winglets. The adjacent stands are heavily utilised and if they were shrunk in size it may create another set of problems trying to accommodate these flights.
One of EDI's many shortcomings at present is a chronic shortage of apron space. There is a current NOTAM stating that runway 12/30 is closed until 23:00 on 12th February due to "Aircraft Parked on block 33" (i.e. the turning area at the SE end of that runway). There was a recent incident (31st October) where an A332 flying a trooping flight was diverted to Leuchars whilst on approach to runway 24 at EDI. It got as far as Musselburgh and, instead of turning onto finals, was vectored down the Firth of Forth towards Crail and then to Leuchars. It had apparently been allocated Stand 17 at EDI because block 33, where they normally park the trooping flights, was already full as was the cargo apron. Stand 17 can only be used when stands 16, 18 and 19 are not in use so perhaps the diversion was because stand 17 was blocked by other aircraft on these stands?
How does Edinburgh hope to attract further long-haul flights when it suffers from such a chronic shortage of apron space? It’s not just the quantity of stands that is a problem. The sizing of each stand is so tight that even B752Ws are difficult to accommodate if there are delays / early arrivals as nearly all of the stands at EDI are too small for them.