Coherent sampling should work, if the frequency is stable and the ping time interval is well controlled. I would assume that both are XTAL based which would get you easily in the 1e-6 to 1e-8 territory on long and short term stability. If it is not XTAL based, then they should change that design, because then you have all the problems you describe.
Regarding filter ringing you will use digital filters anyway. That will give you a long delay, but who cares, you can turn around your ship anytime if you detect something.