According to the traditional Lutheran Confessions, ...
My family attends the smaller of the two local ELCA churches, and my college roommate is an ELCA pastor elsewhere in the Commonwealth. Just FWIW.
(My own theological leanings are more in line with Assembly of God, Foursquare Church, and Vineyard.)
it is unlawful ...
And yet you complain when being called a "legalist."
...for women to publicly "harangue" (i.e. address public assemblies - or even publicly and vocally ask questions)...
This is a non-standard and pejorative definition of "harangue" that suggests bias on your part, or on the part of the aforementioned "confessions," or both.
in a formal worship service or practice any other form of authority over the congregation, like preaching & teaching in church or conducting the service or officiating as a cleric: therefore churches which adhere to the traditional Lutheran Confessions have NEVER allowed Women's Ordination.
Well, then I'm glad my family and friends are ELCA, rather than one of those more stringent groups.
Personally, even the ELCA is way too much like "Catholic-Lite" for me. To me, "high church" formats import an excessive amount of their practices from the Obsolete Covenant.
And I'm not at all sure there is a firm Scriptural basis for the idea of a sharp distinction between "formal" worship services and general gatherings of believers.
According to the author, Harold Holmyard III (a graduate from the Dallas Theological Seminary), when believers are gathered for a divine liturgy in a local church, such a session of the assembly is ipso facto representative of the Universal Church, the Mystical body of Christ.
Naturally, I do not at all identify with churches who believe they find basis for a "divine liturgy" in the New Covenant.
Those who are authorized to publicly address such assemblies (which is commonly called publicly SPEAKING in the assembly) are in de facto and/or de jure divino roles of authority and/or jurisdiction, because everyone else is bound in conscience (under penalty of having desecrated the divine worship) to yield courteous attention. But Harold Holmyard III testified that in such planned formal assemblies, only adult males are eligible to exercise such authoritative actions.
The sort of stringent formality implied here is, as far as I can see, utterly absent from the New Testament Scriptures.
Would it therefore have been lawful for women to serve as Sabbath / Sunday School teachers with adult or adolescent male members of the class, or to direct mixed choirs? Or would 1 Corinthians 14:34/35 and 1 Timothy 2:11/12 have forbidden such things?
By the rules of logic, probably not. But since I reject your premises, I also reject that conclusion.