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When varactor diodes are operated at a lower voltage, their change in capacitance varies at a steeper rate for a given change in voltage.  This is the purpose of removing R187, and the added inductance compensates for running the varactor at a lower capacitance/higher reactance.  The problem you are having is that you reach a point where the oscillator simply shuts down because the crystal load capacitance is insufficient. 


When adding a capacitor in parallel to CT3, you are bringing the pF back up/reactance back down, which does the opposite of removing R187, and as a result, you will once again lose the slide.


You might be able to increase the collector current in the oscillator to help it stay running with the lower pF value, but at the end of the day, stability goes out the window, phase noise goes up, and I think you should just try a different crystal and leave things alone.