I have a thought about Deut 22:5. There is a connection with war.
I think this verse speaks of two extremes:
1) When a woman puts on a SOLDIERS outfit (articles of war). In my opinion Torah prohibits women in participating as SOLDIERS because a woman is a symbol of fertility and peace (sorry if its sounds corny). So it is an abomination unto God when a woman bears an articles of war and participates in killings.
2) The other extreme is also discussed, when a man openly displays his transexuality and wears clearly women's attributes, such as a skirt and/or makeup.
It is an abomination unto God because it is clearly antagonistic to life (man rejects his purpose to procreate because he is gay/tran and he was made in God's image).
The reason that such strange language is used is most likely to cover all possible scenarios, including two extreme ones I mentioned above.
My PREVIOUS thinking was this: (Idea was based upon my MISUNDERSTANDING of the verb "be" used in the passage). Women cannot be tools of war (soldiers/spies/etc). Soldiers (men) cannot wear women's dress (such as in spying, etc).
My CURRENT translational hypothesis is this:
It shall not be that a soldier's articles [are] on a woman, and a soldier shall not put on the garment of a woman...
Something I have considered in support of this is that there are several commands which seem to largely be for the purpose of prohibiting pagan practices (from my understanding). There are a few others but I won't mention them for now. From my understanding, a Canaanite practice at the time in regard to their worship involved women dressing as soldiers for their ritual. If that is indeed the case, it would not surprise me if the command is effectively in response to the practices of the heathen.
The exact implications of the passage are still unclear to me, regardless. The prohibition for soldiers wearing women's garments could be a prohibition on soldiers disguising themselves as women. It could be applied in a greater context of men in general, though I would doubt it based upon the word selection (geber), especially since that would create problems for consistently interpreting the first half of the passage.
What defines "articles of a soldier" is of curiosity to me. Obviously a woman donning weapons and armor for the purpose of behaving as a soldier would likely be violating the command. Would a woman be prohibited from using weapons at all? Pepper spray, for example, would not really seem to be the article of a soldier, but firearms or swords easily could be.
My personal inclination is that a woman should be able to defend herself with a firearm if the need is perceived. However, in the light of the passage, I am very hesitant about that.
My understanding of the passage is that it does NOT say that a woman is prohibited from being/acting as a soldier, BUT instead that a woman is not even allowed to have the articles of a soldier ON her. I would NOT think that the wording of "kilii" would just be referring to the armor or clothing of a soldier, simply because it is applied elsewhere in a very broad variety of contexts, thus I would think it would include weaponry as well.
I would NOT think that i.e a shotgun would only be sometimes considered a soldier's article and then at other times not. For example, fighting in a war with it would make it a soldier's article, but defending livestock from wild beasts, or hunting, or using it for personal protection on one's own property would not qualify it as a soldier's article. I'm not sure, but I hesitate to argue for that view in the example. I would think the shotgun in question either always qualifies as a soldier's article or never qualifies. I don't know.
I am very strongly inclined to think that the command is NOT simply a general prohibition on transvestitism. I think a different meaning is being implied by the wording.
I also wanted to point out that "geber" is used in other verses as well. For example, Genesis 6:4 (plural form) and Genesis 16:4 ( where this word is used in a context of women).
It says in Genesis 2:18, a woman is a "helper". Which means that a woman can share a man's activities. To what extent - that is a good question though.
So if you train your woman to use a shotgun for self-defense, I absolutely do not see how Torah would prohibit this.
The word "geber" certainly has an implication of dominion, as in a master/servant relationship and in other situations (flood waters dominating the earth, Israel prevailing in battle against Amalek, etc). As you stated, it can interestingly be applied to women as well (though a feminine form of the word).
A woman is to be a helper to man, but does that imply taking care of the home or being 100% equal? It's not exactly equal, that much is clear.
Every woman in TNK that killed someone went about it through the use of dropped objects or tent stakes. But Deborah (Judges 4:4) was a warrior.