I would imagine that your McIntosh amp is DC coupled, and these circuits are extremely sensitive to anything even remotely resembling DC appearing at the input jacks. In the Crack, the coupling caps are rather large to work well with headphones of relatively low impedances (compared to the input impedance of a power amp), and those 2.49K resistors on the headphone jack are sized to not eat up much of the output current but to also keep the output of the Crack relatively close to 0V.
If the cathode emission of the 6080 isn't perfectly constant over time, a little bit of DC voltage can appear at the outputs. In a DC coupled solid state amp, that DC would actually be amplified and passed to your speakers, which isn't desirable. Probably the easiest solution in this case is to use something like a Harrison Labs or Rothwell attenuator in the -10dB to -12dB range at the inputs of the McIntosh, as this will cut the appearance of this near DC content and make it less likely the protection circuit will trip. Somewhat by accident, the Moreplay architecture kind of does this on its own.
(Another solution is to just not to use DC coupled amplifiers)
-PB