FWIW, I had an even worse problem- my modem was disconnecting from the service because my upstream signal was, like your, poor. I can't change my splitter situation either. I had an old, unused bi-directional amp laying around, so I tried it. That fixed the problem- no issues since, except on very hot days, I lose my 3 channel upstream bonding. I still get full speed, and no TV signal problems, either.
The amp is a Radio Shack 1 in 4 out bi-directional amp. Costs about $30.
Now everyone will start yakking about how an amp isn't the solution, and Radio Shack is crap. But guess what- it works fine and fixed the problem. Haven't had a disconnect since.