Alarms on a phone system is a bad idea.

Alarm systems have a battery backup so they'll still work during power fail.
Phone systems generally don't.

Also when the internet is down, your sip trunks won't work so it can't dial out.

I've done a lot of testing with this and I've found that the dtmf tones get distorted by the provider so they alarm receiving equipment doesn't recognise them.

You can try using g.711 and setting the dtmf to inband (this emulates a pots line as best as voip can).
You may also have an issue with the voltage on the sli3 card not being exactly the same as a pots line (48-52v DC here) the sli card will likely be about half that.