Your data is 2.4kHz, and you're running the sent and received signals through a phase detector. The propagation (wavelength if you will) is about 12 km. One eighth of that (round trip, 90 degrees) is 40km. So your phase detector gives you 0-Vcc from a measured distance of 0-12km.
2) Using 5V as Vcc, and assuming your timing on the phase detector is set to maximize the slope, your phase detector should give you a voltage delta of (5V/12km) or about 400 microvolts for a one meter distance change. Can you consistently measure 400 microvolt changes? It would require a 4-1/2 digit multimeter, for example, to measure to the nearest meter. Your phase detector power supply should be stable to 100 parts per million to avoid introducing spurious results.
3) Using a timer, assuming a 10MHz clock rate, each tick of the timer equals a round trip distance of 30 meters (round trip 15 meters). That's your basic resolution, assuming a perfect transmitter/receiver..