I think it was a matter of political majority.

What is LTT needed the Hall to approve of his plan? I mean, this was a big deal and they lived in a legal system. What if LTT had a number of women to help him (at least during the earlier stages of his conflict with Latra Pose) but didn't act because the Hall wouldn't approve? What if he needed a 51% vote from the Hall to act?

Then even having the women to help him wasn't enough so long as most women apposed him.

He waited and argued for approval of his plan, but lost the argument. Next step would have been for the Hall to put a legal ban on anyone supporting LTT's plan. That would make it even less likely for anyone to support LTT.

In the end, it got so bad that the Legal system itself was falling apart, and LTT had to act. He could have tried to gather a few women to help him, but that would be risky. It would expose his plans, someone could tell the hall, and a majority of the Hall was against him. What if they gave an arrest warrant against him?

He chose to act with his closest supporters rather than risk having to fight both sides.

That's how I make it work in my head.