Jet,
I find that the upper bass on the AN-E, as well as other Audio Note models, can be a bit bloated, but, it is a very musically enjoyable speaker so, if that is a flaw, so what? I am not as big a fan of the 300b as I am of other small triodes (2a3 and 45) because the upper bass and lower midrange is a bit overblown. But, as you demonstrated, things can be tuned to ameliorate these sort of issues.
I have heard an OTL on the AN-E SEC and the sound was fantastic. I think it would be worth your effort to find an OTL to try in your system. The Atmasphere M-60 should be a good candidate. It is on the slightly leaner side, so it would not exacerbate the tendency of the AN-E to sound a bit bloated. All three M-60s I've heard had a slight bit of buzz or hum, but, given that the AN-E is not extremely efficient, I doubt that this noise will be much of an issue.