From the OP
"I found this to still be the case with the UMC-200. During manual calibration, the subwoofer level appeared to be set about 6-8 dB too hot when using the internal tone generator and my trusty analog SPL meter."
I believe I have figured this out.
I recently switched from a pair of Velodyne ULD15s to a pair of SVS CS-Ultras. The Velodyne's had a built in crossover, originally set to 85Hz, but I had them modified to about 300Hz. The SVS' are just an Amp and 12" driver, no Xover what so ever. The Velodyne's fit the OP's 6-8 dB offset finding, I found them to be about 6 dB hot. The SVS' however were spot on. Using an external test disc, I confirmed the readings.
The problem is, the UMC-200 send a full range tone out to the subs, the test disc, only <~80Hz (what should be in the LFE channel). The test disc, with the <80Hz output, leveled the playing field. Both subs measured the same, but when then switching to the UMC-200 tone generator, with the full range output, the SVS' being "full range" (so to speak) had about 6dB more output than the Velo's, which were capped under about 300 Hz with internal xover. So, not knowing this issue, you would increase the Velo's output to reach the "appropriate" dB, but they would be way to hot.
So it all seems to be related to the design of the sub.