The BwB says explicitly that a circle of six men and six women, being the most balanced possible circle between men and women, was capable of doing some things no other circle could.

We're even told that a circle of 72 at times was weaker than a circle of 12, especially if it was not balanced well.

I assume that the precision advantage any mixed circle gives depends on the balance of the link. A circle of one man and one woman is quite capable of some things that two men and one woman or vice versa cannot do.

So, it seems that LTT did need just six women, and they had to be very strong.

Why not weaker women with angreal/sa'angreal? I think the circle leader had to shift through the operation, and then, one of the weaker women would be called upon to weave stuff, and due to lower dexterity and skill, they would have mucked it up.

Hence, he was left with no choice but to go for it with only men.