Given that you are feeding your Ooma dialtone to a spot upstream from the alarm (line seizure happens, alarm panel still has Ooma's dialtone/line), see if you can find some info about your alarm here:http://www.doityourself.com/forum/elect ... sting.html
This site has lots of info.
Once you get to changing prefixes, try using *98 as well (if you have a Telo).
During times when alarm is calling out (test), phones connected to your walljacks shouldn't have dialtone. This condition may last a while (example, more than 15 minutes; alarm keeps the line seized while re-attempting successful handshake with alarm central). Your Ooma line 1 indicator may go off for a while but when Alarm trys to call again, it would light up again (while all your other phones connected to walljacks don't have dialtone). Depending on alarm panel and how programmed, the reattempts could be as many as 15 times or more before the alarm panel gives up and releases line seizure.