Factoring in 9 when accounting for TE error

I've been using my newfound linear algebra mojo to plunge deeper into
error metrics.

One thing I noticed is that when working with chords like
4:5:6:7:9:11, existing TE optimizations will tend to be such that 9
gets stuck with higher error than everything else. This came up when I
was working with my superpyth reharmonization of the diatonic scale,
in which Dorian, Aeolian, and Mixolydian are the "major" modes, since
they contain 4:6:7:9 triads (which I usually voice 4:7:9:12, as a cue
from Ravel). If you want to look at 4:6:7 and ignore the 9, then
Phrygian becomes major as well.

I noticed that POTE algorithms tend to suggest tunings that give
higher error to 9 than everything else. For example, the 2.3.7
subgroup 64/63 temperament is

http://x31eq.com/cgi-bin/rt.cgi?ets=22%2C+27&limit=2.3.7

The POTE generator is almost exactly that of 27-equal. However, the
9/4 in 27-equal is irritatingly sharp (20 cents sharp, in fact), which
is double everything else - everything else tends to have about 10
cents of error. I assume that this is because TE tunings tend to
optimize for 2, 3, and 7 (at least the part of the algorithm that I
understand seems to do this), and once you have a decent spread of
error between the primes, things like 9 end up with double the error
as everything else (or at least double the error of 3).

The hexad I usually use for 11-limit chords is something like
4:5:6:7:9:11, not just 4:5:6:7:11, and optimizing in that fashion
tends to throw 9 off in relation to everything else. So I wonder if a
good alternative might be to optimize all integers up to the
integer-limit of whatever prime-limit you're working with - e.g. so
that if you're in the 11-limit, the full chord 1:2:3:4:5:6:7:8:9:10:11
is used. At one point, the subgroup 2.7.9 suggested 22-equal's fourth
as a generator, which is closer to this ideal. But it looks like some
of the recent recoding of the temperament finder has broken this,
which I'll point out in the other thread about bugs. But either way,
is there a name for this sort of thing, and do I have the right idea?

-Mike