TL

“They don’t seem to have any reason for thinking that being created first gives one authority, apart from “God says it does, in 1 Tim 2:13?. “

Well, Paul does not say that God says it does. Paul says the he, Paul, is not now permitting something. This is not how God institutes a divine new (NEW, not used before, never before stated anywhere in the OT) law.

“They see the fall related to the reversal of the creation order. “

I don’t understand this. If they believe that God made the male to rule over the female in the ‘creation order’, then a reversal would be God making the female to rule over the male. If they don’t believe that there was any ruling over one another in the creation order, then a reversal would be both trying to rule over the other, which might make more sense. However, that does nothing for their case as it does not institute a male over female order. In reality, there is no rule in the OT for men to rule over women. There is only the law of ungodly desires for the powerful to control the weaker.