Is this typical of any hdmi monitor, or might OP have a particularly leaky setup?
It would be nice to see if this setup is FCC compliant. Often devices like this are tested under one set of conditions (eg. Screen resolution), but might be wildly out of compliance when used with a longer cable, with a different screen resolution, near a wooden table (which changes the impedances and can cause something to radiate which otherwise wouldn't)
Hoo boy, this brings back (bad) memories of emissions testing HDMI.
Back in the days when I worked in consumer audio, we were working on a small sound bar that used HDMI for sound transmission via ARC. However, the product folks were worried about compatibility with SPDIF only TVs, so asked us to design a little HDMI to SPDIF dongle to allow this soundbar to work with SPDIF TVs, or HDMI TVs with no ARC support.
Long story short: the compliance test folks were only testing with the SPDIF/ARC dongle. Due to a quirk of this (I think not being able to read an EDID from downstream?), the processor would shut off the HDMI interface. No TMDS, this; little to no emissions.
We all got a nasty surprise when we hooked it up to a monitor and ran it in the test cell again. That was a big scramble to fix.
Funnily enough, it was only at the highest bitrates (which I think was 1080p) that emissions were problematic. All the lower bitrates passed with no difficulty.
It would be nice to see if this setup is FCC compliant. Often devices like this are tested under one set of conditions (eg. Screen resolution), but might be wildly out of compliance when used with a longer cable, with a different screen resolution, near a wooden table (which changes the impedances and can cause something to radiate which otherwise wouldn't)