If you are switching by enabling VCC to other parts of the circuit, try simply adding a resistor between the switched VCC and the tuning voltage, maybe adding a series diode if there is risk of current flowing back. If that gives the wrong shift direction, use the switched VCC to bias a transistor and connect it's collector through a resistor to the tuning voltage so it pulls it slightly down. I appreciate that with such narrow tuning range your shift is limited but that would always be a limitation when pulling a crystal.
Brian.