Jim,
I used a XTRX SDR that has two phase-coherent channels. A USRP or LimeSDR could also be used in the same way. Additional requirements are that the LNBs are modified to accept a common 25 MHz reference.
While I haven't tried one, I think that a KrakenSDR should work well also since only ~ 2 MHz of bandwidth is needed to capture all the Doppler shift from the narrow band beacons.
I'm looking for signs of Doppler scattering from the carriers that might occur from rain scatter. I think it should be possible to detect forward scattering from aircraft too.
David