A lot of misinformation in this thread so far....
1: The amplifier tubes do not need to "stabilize for 30 minutes" to prevent the radio from drifting, this is absurd, no offense to the person who stated that.
2: The power supply voltage coming from the 120 VAC outlet dropping should in no way cause this either because the radio will maintain a constant 13.8 volts to the circuits, or 8 volts, or 5 volts depending upon the section of the radio due to internal regulation.
3: The frequency counter should not change frequency with your voice on this radio because of the way it samples the operating frequency.
4: My guess is that RF is getting into the freq counter itself, and if the radio in fact itself is drifting, I would suspect RF is getting into the board and affecting the regulation, VCO, or PLL circuitry. Better RF bypassing on the amplifier, spacing the amplifier farther from the radio, and RF ferrite chokes can help this.