"The original version of the JD9 has trim pots that can be used to dial in the gain when using the low outputs. I pulled out my multimeter to balance the channels and got readings of 18Kohm and 12Kohm on L/R channels respectively. Using the pots, I balanced everything up - no problem."
You seem to want to talk about signal level, which is typically given in terms of voltage, and here you quote values for resistance that don't make sense to me. In addition to getting the units correct, what are you measuring here? The resistance across the phono inputs? Or what? I am guessing maybe you have measured the resistance across some RCA jack that is affected by the attenuators. Maybe one of the output jacks??? Thus one channel can read different from another, depending upon the setting of each attenuator. This is normal, but it tells nothing about gain or signal strength. Usually, if all the tubes are in good shape, the resistance afforded by the attenuators would end up about equal, for equal sound pressure levels between channels.
Then you write, "My integrated expects 47KOhm input, but I expect that the line level signal jumps all over the place." I don't know where to begin, but the cartridge probably expects to see a 47K input resistance. Perhaps you are here referring to the phono input resistance, which for an MM should remain an invariant 47K ohms or higher, but the same in both channels. The Jolida doesn't "expect" 47K ohms; it provides 47K ohms for MM cartridges. The 47K resistors are in the Jolida phono stage, at its input. wired from hot to ground.