If 2-5 aircraft a day is norm and that is acceptable, then I would suggest that when you're getting 20 a day, this is because Heathrow has directed the traffic that way for reasons already explained. This indicates that, unless ATC directs otherwise, the pilots are taking a variety of routes.
I still maintain that the best way of dealing with the problem is one of mind over matter. For example, I used to have the screaming ab-dabs if I saw even a money spider. However, I realised that my fear of spiders was almost ruining my life so I took steps to deal with it. I still don't like spiders but I can look at photos of them, tolerate being in the same room as one and even, with my super spider catcher, catch one and put it outside.
I saw it as my problem and dealt with it.
Alternatively, as TotD suggests, you could get up on the roof
Cheers
Whirls