I will repeat my suggestion of the Antennas Direct C2V. It is far less directional than bigger antennas and you have a lot of fairly strong signals in your area. Lots of gain isn't what you need and an antenna that can pick up signals off the back reasonably well will definitely help. Put it on the roof, use the shortest coax run you can get away with, go without a preamplifier since the stations in green will overload it. Put it as high as you can outside. The good news is this is a very small, light antenna so it's easy to manipulate and it won't disturb the neighbours. I'd start by pointing it SSE and see how that works. It covers a fairly wide spread so that should get a lot of stations. Try adjusting it a few degrees at a time to find a sweet spot that gives you the best reception.
To give you something to compare to, here is my TV Fool report:
http://www.tvfool.com/?option=com_wr...2c1573a1a67363 Look where channels 32 and 35 are on that chart. Those stations are the ones that I didn't receive at all indoors and I now receive about 90% of the time with that antenna outdoors. I did try a DB8e, the flagship Antennas Direct antenna, and it was no improvement. I actually lost stations. I'm going to experiment with it a bit more but I am not hopeful. The C2V, OTOH, rocks despite it's small size, pulling in stations from a wide swath of country around me.
I just watched PBS Newshour on channel 32. Your channel 40 should be easy by comparison.