I will opt out so that other of our experts here can see your question.
Unfortunately some engineering will be required, and a CAD drawing, and parts specification, that will take 2 hours or so, so you may not get any takers.
Since there are not any 30 amp rated wall mount heat only thermostats, there is no simple answer. In that case I am opting out. Others here may have the answer you seek.
some design services will be required for a remote contactor conversion, that is the best solution that I personally am able to provide,
I hope that addresses your confusion. (the difference is between just a single answer, and an engineered solution)
Now here is the verbal description I promised you:
1. Mount a 24 volt transformer, and 40 amp contactor in a 10 x 10 x 4" electrical box near the source of power for the base boards.
2. Bypass the existing thermostat wiring by using wire nuts so that the base board gets power 24/7.
3. Then wire the contactor to interrupt that power, and control it with a 24volt thermostat mounted in the room with the baseboards.
I will opt out, so that you owe me nothing for that solution, let me know however if you want me to provide you with an engineered drawing and parts source specifications by accepting my offer.
Good luck with it,