The good news is that if your power is reduced by 6 dB, no RFI. So the problem is probably easily solved. You say you have ferrite chokes on your coax. What type, how many turns ??. A few decades ago I had RFI both to and from an old CRT TV set. The RFI is very bad on 160 meters, less on 80 meters, and little or none above 80. I put about 10 or 11 turns of coax (RG-6 or RG-59 ?) on an FT 240-43 core, on the TV coax feed. Reduced RFI by over 10 dB on 160 and even more on the higher bands. FT240-31 would have been better for the lower frequency bands. Since my problem was bad, I ended up using three chokes in series very near the TV set, solved RFI in each direction completely. IF your signal is getting into the TV via the TV coax try a new cable box to TV jumper cable, and put at least 10 turns of that coax on a core, should give you well over 15 dB of attenuation on most ham bands. Also a possibility of the cable feed from the provider into the cable box, put some turns through a core. Also start out by simplifying your set up as much as possible. Just run one TV at first, no splitters, etc. Also in your ham shack just simplify things, no coax switches, SWR meters, etc. If any of that solves the problem, just add things back one at a time. It is very possible that one of your ham or TV coax jumper cables is bad which does happen (occasionally) for both home brew jumpers and commercially pre assembled cables. Recently I had an RFI problem due to my 6 port (remote) antenna switch which had a slight (one ohm) DC resistance on the shield connection on one or more of the connectors on the switch. This was an expensive switch !. It was a design fault, so I disassembled it and did my own modification. Good Luck Rick KL7CW