A Solution? You could always ditch LHR and interline through Schiphol. It might be in another country but you can be there in the time it takes to get from the gate to the LHR long stay car park.
Heathrow is an absolute shambles and it always will be. I can't see that T5 will alleviate any of the problems, merely move them to another part of the airfield. T5 really is going to be just a nice shopping centre for the BAA!
The big problem is crossing the runways at peak times. Maybe the LHR management ought to look to other big airports to see how they achieve it. There are seldom the sort of problems at Frankfurt, even if you don't get to land on the Lufthansa runway you can still get to the gate reasonably expeditiously. At Schiphol, you might have to taxi a similar distance as going to the moon, but at least you can cross the active take off or landing runways with the new taxiways around the protected ends of the runways.
LHR's problems will always be a political bugbear and unless someone stands up to the NIMBY's and flattens a large portion of Hounslow there will never be any improvement. If you can't spread out on the site then it is surely time to reconsider Heathrow and either make it a long-haul only base or short-haul. What London needs is a NEW dedicated super sky-port and it is only the politicians who could achieve that by standing up to the Greens and their ilk.