[Electronic M]

Some of the solid state sets are more tolerant of signal hum. That said you should be able to make the hum almost unnoticeable either through recapping the Blonder Tongue, the TV or by breaking ground loops. My main BT rack I run on an 120V isolation transformer with the ground prong disconnected... It's fed by a rack containing about every consumer video tape and disc format to ever be popular as well as some digital sources....One of those digital sources (a PC) had a grounded power cord that I had to also break the ground connection from to stop hum...That PC eventually got upgraded but I kept the cord that way for its replacement.

One thing you have that I don't is a wired RF connection. All my modulators feed antennas and all my TVs have antennas. The spaghetti mess I'd get it I tried to connect 100 sets across 3 floors and more rooms would be insufferable....One thing in wireless mode is sometimes if there's a large metal object (metal cabinet roundy, refrigerator, etc) for the signal to reflect off of the distance of either antenna relative to it can cause hum, signal cancellation and other oddities.... It's possible to achieve the same effect with a wired system as well...If the coax is not the exact impedance the system is designed for such reflections become possible, and their severity varies based on cable length as a function of RF signal wavelength...More speciffically fractional wavelength....The effect of 3/4 wavelength is different than half wavelength, but 0.5, 1.5 and 2.5 wavelength coax lengths should behave roughly the same. The advantage wireless has over wired is it's easier to find and adjust out reflections than coax....The disadvantage is that when things and people are moving around the house your optimal adjustment changes (sometimes just from someone walking or where in the room you sit).
RF is a strange and interesting world...