I put my flat in the UK on the market recently and it has given me a lot of insights into how broken the real estate market is! One thing I found particularly annoying is how dominant rightmove is and how much of the traffic for house hunting they control.
As a small way of standing up to them I created https://rigove.co.uk/ (rightmove without htm - the hidden toll machine ;)
If you change rightmove to rigove while browsing a property for sale you get a page which shows where else that property is listed.
It is only a few days old so it is currently more miss than hit but I plan to reach out to estate agents to increase coverage as quick as I can.
I suggest considering a different domain name before this gets too popular. Rightmove might call it trademark violation for the name being too close, if they get annoyed at the competition.
I'm genuinely curious - are you saying this because you know quite a bit about trademark violation?
I know almost nothing about trademark violation and agree it's likely a risk. I'm in the U.S. though.