OK, 105 watts into 8 ohms is 29 volts RMS. Speakers are 89.5dB/w/m so a nominal peak power of 102dB would require 11.9 volts. Amp gain might be 27dB assuming the Bel Canto is in fact identical; that's a factor of 22.4 so the peak input you need to the amp is 0.53 volts.
Stock Quickie gain into a high impedance is 2.2; into 10K I would expect about 1.8 gain. Assuming your source has a peak output of 2vRMS, it would be possible to generate 3.6 volts RMS output peaks. This is about the absolute maximum output from Quickie with fresh batteries, so turning up the gain on Quickie can result in clipping if the batteries are worn.
With depleted batteries a stock Quickie can put out about 2.2vRMS, which is 12dB greater than the needed 0.53 volts. Hence an input attenuator of up to 12dB at the power amp input would allow the Quickie to appear less microphonic, at the expense of pushing its output capability (increasing distortion).
Personally, I would opt for tube rolling and vibration control to get the microphonics down - 12dB is not that great. I might try a 6dB input attenuator as an experiment. You might also experiment with passive preamps as well, since you do not need gain in a preamp - again, assuming your source has 2vRMS peak output.