You're absolutely correct about the M4 and M5 being well used corridors for passengers in the Bristol region seeking long haul from LHR and BHX (I use London for long haul and have used Birmingham too), and this is almost certainly why the BRS management in its master plan believes that scope for long haul scheduled services is limited, apart from the physical constraints of the airfield.
As for the Middle East, last autumn the UK manager of Qatar Airways, Richard Oliver, said his airline was looking at serving South West England - see third paragraph in attached link.
Qatar Air Mulls Gatwick Route as Heathrow Flight Upgraded to 787 - Bloomberg
Of course, looking to do something doesn't mean that you will but it does suggest that Qatar at least recognises there is a potential market worth looking at in the South West. It needn't necessarily be BRS; it could be CWL or even EXT.
Continental lasted five and a half years on BRS-EWR and eventually moved the service to LHR to become their fifth daily EWR rotation. They didn't have LHR access when they began BRS-EWR in May 2005 and cited the recession and poor take-up in the business-first cabin as two of the main reasons for the move.
BRS management has been quite public in recent years about talks with airlines to reinstate a NYC service and last year said that talks were at 'an advanced stage' with the expectation that a route would commence this year. It was assumed that the airline was United or American, or perhaps both.
That the route did not come about may well prove your comment correct but, again, there seems little doubt that airlines are at least exploring the possibility.
My own view, and it's shared by some acquaintances, is that long haul airlines are awaiting the decision on devolving APD to Wales (where it would be cut to nil according to the Welsh Assembly Government) before making final decisions whether, and if so where, to operate such flights from Severnside.