Smart TRVs with Intergas Thermostat

I have no idea where else to ask this, so here goes. Maybe someone has run into the same issues as me.

I have floor heating on my ground floor, connected to my boiler and a thermostat in the living room. I can read (and set) this thermostat from within HA (Intergas Incomfort).

I will have 2 radiators in other rooms, with smart radiator valves (Aqara E1).

Now my dilemma is how I can ensure that the boiler goes on, even if the living room is already the right temperature, but the other rooms do not. Theoretically, with the smart system, the Intergas gateway should be able to tell the boiler to run since there is heat needed elsewhere, and then I can maybe use a different system (smart plug??) to just disable the floor heating pump.

But this all feels like a hack. I am renting my boiler, so I can’t change to a full ecosystem like Tado that includes the living room thermostat as well.

Any tips, ideas?