Realistically, the best option if you want to use a single frequency is a PLL, for example the NE565. It will not only do the filtering for you but provide a digital output you can use directly without needing a comparator at all. Just set its oscillator to free run at 2200Hz and use the lock detect output to drive the UART. You can control the bandwidth and response speed with the loop filter components.
I don't know what your application is but my fear over using a single filter and AM detector is the noise immunity will be very low. I appreciate your comments about the line being 'clean' but phone lines are prone to picking up static in storms and they don't guarantee the levels will always be the same. If you do want to follow that path, a simple half wave rectifier will work as well as anything else but be careful to keep the time constant short so the output pulses don't run into each other.
Brian.