Unfortunately at Heathrow with the noise abatement procedures that are in place, a request like this will be given an answer of "No", especially when westerlies are in use. At many airports, ATC hands are tied regarding which runways they can actually use with respect to noise (like the good old 1500 alternation).
As you probably know if the inbound delays are excessive, both runways may be used in certain circumstances, but some big-brain at TC is frantically working out an ideal order as who to put on the other runway (wake turbulence isses, where they're parking etc)
Sorry mate.