"Forget about replacing these coils with whatsoever. The EM circuits are designed to take into account the (relatively) low parasitic capacitance (and thus the elevated SRF) of the 3-Pi wound Mouser 63xx series coils. The only confirmed working replacement are the Hammond 1535 series coils. With all other approaches you will have bad linearity or a restricted pitch range, or both." - Thierry
As an experiment I picked a coil I wound some time back that measures 9.105 mH with my LC tester and 94.5 Ohms DCR.
I directly stimulated one end of a coil with the output of a function generator, and hooked one scope probe to this as a reference. The other end of the coil was left unconnected and a second scope probe placed some inches away. The coil was placed on top of a small plastic box to distance it from the workbench. With this arrangement the self resonance is 850kHz and the -3dB bandwidth is 7.2kHz, which gives a Q of 118. I'm pretty sure the Q is a bit higher than this because the function generator output is 50 Ohms (which damps things). And I'm sure the self resonance point can be made a bit higher because the center tap wires are just hanging out, as is the passive end, which increases intrinsic C.
I don't have a 10mH Bourns 6306 to compare it to, but the datasheet lists an SRF of 0.71 MHz minimum and a Q of 95 (measured at 79.6 kHz, whatever that means [EDIT: I suppose it means if the L were padded with a perfect parallel C to resonate at 79.6 kHz, the Q of the combo would be 95]).
I do have a 50mH Bourns 6310 on hand, the datasheet lists an SRF of 330 kHz minimum and a Q of 100 (again, measured at 79.6 kHz). With my setup I measure a self resonance of 470 kHz, a bandwidth of 14.9 kHz, and a Q of 31.5 (at self resonance).
From the above, I think it's fair to say that one probably could replace the Bourns inductors with single layer air core solenoids, perhaps a series of them to keep SRF high, though series resistance might have to be added to kill the Q if that is an issue. But what do I know.