yes , I understood that RMCM01 is a self-contained receiver so this would allow us to leave the polar heart emitter close and have a second device converting 5Khz to bluetooth (even better in my opinion )

As you mentioned they are some alternatives but they are quite expensive (39.9E) which contradicts the project idea.

I will do some more research if there is any website still selling the RMCM01 chip because it is so cheap 4.5E.

Does it means you are no more interested of hacking the device because you are not sure of compatibility ?