I second both of Mofi's comments, Rob.
Your speakers are not especially hard to drive, as can be seen from
John Atkinson's measurements of their impedance characteristics and sensitivity. Given that, and given that the problem occurred even when the speaker's built-in class D amplifiers were left unpowered (so that their fluctuating AC current draw could not influence the PL amp, perhaps by affecting the line voltage), what it all suggests to me is that the PL amp is marginally stable at very low frequencies when it is operating with essentially no load at very low frequencies. (The input impedance of the amps in the speakers, in combination with their associated low-pass crossover circuits, is undoubtedly vastly higher than the input impedance of a fully passive speaker, and hence represents a negligible load).
Whether or not an electrical feedback loop that is marginally stable at low frequencies will motorboat (i.e., oscillate at very low frequencies) could quite conceivably depend on minor variations in the gains, low frequency bandwidths, and other parameters of the parts and circuits that are in the loop, including the power tubes. And also on the setting of the volume control, if it is within the overall feedback loop or if the volume setting (and consequently the amount of power being supplied by the amp) has significant effects on internal operating voltages and/or the AC line voltage.
Given all of that, I wouldn't be surprised if the problem could be resolved even with EL-34s if you were to put a high-power resistor of say 30 to 50 ohms or so across the output terminals of each channel of the amp. That would provide the amp with a somewhat reasonable load at low frequencies, while drawing fairly little power at higher frequencies compared to the power draw of the speakers. A resistor of those values that is rated to handle 50 watts would provide plenty of margin in terms of power handling. A "non-inductive" resistor would be preferable.
The bottom line, though, if my analysis is correct, is that anyone contemplating using that PL amp with any speaker having a built-in low frequency amplifier (which would therefore present a very high impedance to the PL amp at low frequencies) should proceed with caution.
Best regards,
-- Al