Interferometry's arch nemesis: CLOCKS
There are several alternatives.

The first is to go for some form of common clock distribution. But not all ways of doing this are obvious!

The second is to go for a short enough observation, and high enough accuracy clocks, that the accumulated phase drift over your observation is within your interferrometry reconstruction budget. 

Taking the second option, your potential clock sources, from very low cost very low accuracy, to very high cost very high accuracy, go roughly RC, LC, ceramic resonator, crystal, TCXO, ovened crystal, rubidium, caesium, and atomic fountain. Match your accuracy budget with your financial budget, and see whether there is a solution.

When using clock distribution, first consider how it's used on each PCB. Each PCB can either use the distributed clock signal directly, or can have a slave crystal oscillator, which is PLL'd to the distributed signal. This will degrade the long term phase error due to PLL noise, but will clean up any high frequency phase noise on the distributed clock, and can potentially allow a much greater variety of synchronising sources.

Options are many - a coax cable from the master oscillator, or it could be a radio signal. Optical distribution is also possible. Alternatively each PCB could use a GPS receiver, or a receiver for some other radio service.

Finally, each PCB could be entirely free-running, as in the first option. However, you could broadcast an in-band fake radio object signal with known characteristics, visible to all the antennae, often called a beacon. This signal must be small enough to not eat into the dynamic range of the receivers too much, but large enough to be well out of the noise. Demodulate the beacon, correcting the phases of the local clocks to give the sharpest picture. Now use the same clock phase correction to reconstruct the rest of the picture. As the beacon is known to be stable, long averaging can reduce the amount of beacon phase noise that will be impressed onto the clocks. 

This latter one uses the same concept for the way adaptive mirror telescopes can look through an unstable atmosphere (arguably an optical interferometer with poor phase stability across the aperture) and correct the image, they move the mirrors (alter the phase shift of different paths) for best reconstruction of a laser-transmitted guide star.