I don’t have one of those systems; but I do have a possible solution, and it works for me, although (thankfully) so far I have not needed to use it.
I have an Apple Watch, and if I fall , the watch can sense it, and it will ask me if I need help. I can say yes or no, and if I don’t respond at all, then it just calls emergency help and also alerts my emergency contact numbers.
If I need help, but haven’t fallen and activated the alert, there is an emergency button on the side of the watch, and if I push and hold that button, then it calls emergency just as it does in a fall.
Since the Apple Watch is also a phone, I can just call for help using Siri, assuming that something happened and I am still coherent and can talk enough to make a call.
The Apple Watch also monitors my heart rate, and will show if my heart goes into tachycardia or arrythmia, and it will soon be able to also do an EKG right from the watch, and send it to my doctor.
To use this, you will need an iPhone (any series after series 5, so used is okay), and you will need a new Series 4 Apple Watch. The older ones have some capabilities, but not nearly as much as the new ones have, and you will spend around $400 for the watch.
So, even if you spent another $300 for the phone (which would get you a fairly new iPhone) , it would be a 1-time cost and not for just a year usage , and it would replace having to have the alarm system as well as the landline phone.
Another thing to think about is that your medical alert system depends on your home phone, but the Apple Watch will work anywhere, so you don’t have to be home for it to protect you and call for help.
