i had exactly the same dilemma before getting unifi but it's all good now without having two bills. here's how.

i believe your alarm system is connected/hacked to your existing copper cable, right?

to solve your problem, request the TM technicians to connect your existing copper cable to the BTU and it's done. make sure all copper cables in your house are connected to the cable that is going to the BTU. all existing phone ports in your house then can be used and making calls with the new phone number. after that you can terminate your old number.

pm me if you need more clarifications.