I think it's somewhat ironic that those currently living under the flightpaths object so much; building a new runway could actually bring them some relief. Also, a shorter runway with strict performance rules (e.g. 5 degree descent paths and steep climb performance) would help to keep a lot of the traffic away from populated areas; as that runway is north of the current airport, approach paths could be kept well north of the city. They could also be alternated, with various traffic patterns designed to keep traffic away from built up areas, on takeoff and climb.
We know that aircraft like the Embraer E-jets and A32X (ok, just A318 currently) can descend on 5 degree glidepaths and the BAA and CAA can work with manufacturers of current and future planned aircraft, to make sure that their aircraft can meet the new tougher requirements, so that when the new runway is opened, the Bombardier C-series, 737 MAX, MRJ, A32xNEO and various other types can fly in.
There is a LOT that can be done to relief noise pressure from areas around the airport and R3
is a key part of this. It's unlikely that the runway would be opened this decade, so there's a long lead in time in terms of new technology which can be used to the runway's advantage. The big danger is "mission creep", i.e. gradually stretching the runway from its current planned c.6,000' to 7,000', then 8,000' etc etc; focus on getting the runway built and it being a shorter runway for feeder types. That way, it's going to be far easier to set and meet noise targets; an A380 at MTOW is not going to be a great climber! You're always going to have a core group of people who will be vocal and who will oppose any new development no matter what, BUT by being focused from day one on assuaging the reasonable fears about greater noise, there will be a much great chance of success.
I do agree, however, that in order to optimise the use of all three runways, a new terminal will be required to serve the new runway, so that crossing of 09L/27R can be kept to a minimum.