Cross dressing to get out of war - Deuteronomy 22:5

I've been marking this week, and the set passage includes a verse which people often laugh about because it's so weird. It's the (in)famous prohibition against cross-dressing, which is normally translated as follows:

A woman must not wear men’s clothing, nor a man wear women’s clothing, for the LORD your God detests anyone who does this. (NIV11)

It's a pretty straightforward verse, two parallel clauses followed by an explanation:

A     A woman must not wear men's clothing
A`    and a man must not wear women's clothing
B            for the LORD your God detests anyone who does this.

But when we dig into the Hebrew there are a couple of extra features which are obscured by the translation:

1. The word order in the first two clauses is (1) prohibition, (2) man, (3) woman. The only real difference is the placement of the word for clothing (which are different, see below), which in A comes between (1) and (2), and in A` comes between (2) and (3). 
2. The word for clothing is different. In A the word is כלי, which is elsewhere translated vessel/cup or weapon or article. In A` the word is an unremarkable word for clothing/garment.
3. The word for man, in contrast with the usual word for woman or wife, אשׁה ('ishsha), is not, as we might expect, אישׁ ('ish) or even the broader אדם ('adam), but גבר (gever), a word which often has militaristic connotations - "warrior" works well in lots of contexts.
4. The word for getting dressed is only there in A`, it's just the verb "to be" in A. 

All this suggests to me that perhaps it's not (just) a command against cross-dressing, although that wouldn't be massively out of place in the Pentateuch, especially when you consider other commands against gender confusion (note that in a few verses the command will be against unnaturally mixing seed, animals and fabric). But additionally, I think that there's a very real possibility that preparations for war are on the horizon, as they are about to cross over to take the promised land by force. Rather than a man's clothing, it could be the armour or weaponry of a (male) warrior. As such, the verse could reasonably translated to prohibit women from fighting in the place of men, and to warn men against escaping by cross-dressing:

A     The equipment of a man shall not be upon a woman,
A'     and a man shall not dress [in] garments of a woman
B            For an abomination [against] Yhwh your God [are] all these deeds.

Mulan, then, would be in trouble, and while Mrs Doubtfire might not be the explicit target, trying to get out of wartime duties by cross-dressing is an abomination to Yhwh.

Duane Christensen (WBC) notes that these chapters are focussed around "four central issues: warfare, marriage, social ethics, and humanitarian commands." (2002; p466) This verse then could be not so much about marriage as it is about warfare, shaping Israel to be a nation who are prepared to fight for the land to which Yhwh has brought them.