Close Oscillators Problem
It sounds like you have more than one high Q tank oscillators in close proximity and close frequencies.  If the coils are in the same orientation inline or near fringes then they couple weakly like a transformer and will track the one with the higher current flux if within the bandwidth.  

The physical layout and stray capacitance also affect everything so we are blind to the real issues.

The Q is simply the impedance ratio at resonance.

Q=Req/Zc(f)   Since there are two R’s as shown you can have collector only with Q=100 in this example or both for Q=50. Q1b=Q2c are on the same node.

Q is the effective gain above Q=1 and AT crystals have a Q in the 10k value.

Upon reading your edits of purpose it sounds like a lot of improvements are needed with details missing.

Added

GDT’s go from low pF to low Ohms thus over dampening the Q like an SCR crowbar.  Not good.  A linear TVS may be better with heat managed somehow.