You cannot really compare commuting by "normal" vehicle to commuting by heli, if I need to explain why then there really is no hope........
I'm not "anti anti", merely matter of fact. Helicopters are now quite a normal way to travel for some; especially in your area, you don't need to explain anything in that respect.
We all also know that helicopter noise can be intrusive; I certainly know that, after earning my living flying them and living near them for thirty years. If they and other aircraft were quieter, many of us would be happier, including me. I actually live under three "flight paths", one used by light aircraft at less than five hundred feet, one used by airliners operating in and out of a regional airport and the other used by transit traffic, mainly helicopters being vectored at similar heights to the ones you experience, to avoid the airliners.
If I were of the same mind as you, in a different financial climate I could try putting my home back on the market, albeit at a large financial disadvantage because the planning issue affecting me has come to fruition and has badly affected my property (devalued it by 30% according to the surveyor). The sale of it fell though in the past because of the then impending planning issue.
I'm not sure what you
do actually want us to do about your problem. We are constrained where we fly, by the law and by other factors and are only going about our legal business. Aviation is already one of the most regulated industries. You should realise that we as individuals on this website cannot do what you want with respect to monitoring helicopter movements, any more than could (or should) a driver monitor motorway or other road movements to appease a complainer.
Edit: You are perhaps aware that other helicopter routes are available into the LHR control zone. There is another route inside the zone, (H3, you perhaps now have an aviation chart because you already know about H7). Normally many helicopters route north of you along there. However, for aircraft separation reasons that route cannot be used if Heathrow is using their easterly runways and they will do this if the wind direction so favours. In these cases, aircraft will have to go along the south sideof the zone and so you will hear more of them. I'm very surprised you make a complaint here if you only hear 5 aircraft in a day!