Hello Harry, and sorry for the delay in replying. I decided to bite the bullet and go for a digital modulator, in line with previous advice from Nodrogd.
So I bought on eBay a Triax MOD103T box. Got it for about £65 (new price about £200, which I didn't think I could justify). The RF output from the Triax connects into my aerial feed and can be used by a TV anywhere else in the house that is connected to the aerial RF system. Of course those TVs would need a tuning scan to pick up the new signal at channel 900 (or whatever). I could have just fed the HDMI through that box and connected the pass through HDMI cable to my TV. That would just have allowed me to replicate the output from the TV360. But I added a splitter to the signal from the TV360, and then fed one of the two outputs to the TV, and the other to the input of a 3-way switch which then connects into the Triax. Other feeds into the 3-way switch are my old Apple TV Box and my BluRay player.
So I can now watch these other feeds on the kitchen TV, or watch the TV360 output.
The picture on the kitchen TV is excellent. However the sound was just a horrible buzz. I seem to have fixed this by changing the Audio settings on the TV360 box to PCM2.0. This might mean that I now have suboptimal sound out of the box, but frankly I haven't noticed. It works beautifully and I'm very pleased with the outcome.
Harry, you mentioned the buzzing problem with your analogue solution - it may be worth trying to change the TV360 audio settings from Auto to PCM2.0.
The only frustration that I now have is that there is about a 1 second delay in the signal at the kitchen TV compared with the main TV, presumably due to the digital processing. I can live with that.