I confirmed that your sub does in fact have a high pass filter. I was surprised. It's the slope of the low pass filter that would interest me. On a THX rec'r that slope is 24 db/oct. I use to have an old H/K with a 12 db/oct slope and I found the sub channel to be too localizable (or whatever that word is) for nearfield use.
It's just a question of which crossover you want to use. YPAO will have EQ'ed that signal either way. I guess you're making you're rec'r amplify the LFE too but there isn't any draw on it. Anyway, my inclination would be to let the rec'r handle the bass management and then get a shielded coax to get that crossed signal to a sub.
Either way, YPAO's control of the 62.5 Hz frequency is still executed in the sub. I'm not clear on why you say YPAO will not EQ the sub. It would EQ the sub out channel the same as the speaker level outputs. The differences you're encountering with speaker level connections is the use of a different crossover and I think speaker cable is more prone to RFI/EMI.
I think it would be interesting to see the difference to take note of the YPAO values both ways. I wouldn't run speaker wire to a sub and I haven't seen anybody else do it either. I do seem to remember folks with bigger brains than me saying not to do that as well. However I do have a great admiration for people that never listen.