I have a project that requires that I detect disconnected phone
numbers without actually ringing the person (i.e. at night when we are
not allowed to call customers). I cannot find anyway to do this with
my PBX or through any third party services. Any solutions?

As far as I remember, ringing current is around 130 volts AC. As long
as you stay well below that, you should be able to measure the current
flow for an applied voltage, and calculate the resistance.