Thanks for a thorough explanation of your cellular network surroundings, such things really can help understanding why a device doesn't work as expected.
I don't know enough of the innards of a modem, cellular or wired, to be able to tell exactly what's going on. However, they're small computers running most often a version of Linux so the common issues known from computers and phones should apply. One such "law" is that if the processor has to work harder to produce a certain performance level it also produces more heat. In this case the hard work is communicating with the tower. As you said, you would be able to see the tower if the trees weren't so tall and as I said in my first post trees have quite a lot of water in their leaves which can have a negative effect. But that's not the only explanation. Accepting a slightly weaker signal through reducing the transmission power as you did might well be the optimal solution - although modems are computers they aren't as sophisticated as "real" ones, meaning they don't have adaptive power handling and such. Most likely the default setting is "full power" be it needed or not. The law of conservation of energy applies here as well.
A leading Finnish PC magazine had a couple of articles about underclocking last year, comparing performance loss to energy consumption. The most dramatic finding in their studies was that when the CPU max power was reduced by 25% the energy consumption was halved! Going down to 50% lowered the used wattage only about 10% more so exaggerating the underclocking level will only hinder performance. The conclusion was that if the ultimate max power isn't needed, a slight underclocking won't affect everyday use but the heat level will be dramatically reduced and the energy bill will be lower.
