modifiers and other things embedded in a Latin phrase

Latin Learning Latin
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Does anyone have any good strategies for learning/teaching the skill of reading and understanding in a natural way a Latin phrase that has modifiers or other words embedded in it? For example:

Caesar, Civil Wars:
Reliquiae copiae missis ad Varum noctu legatorum numero centurionibus sese ei dediderunt.
“The remaining troops, having been sent to Varus by night of envoys with the rank centurions, surrendered themselves to him.”
i.e., centurions having been sent to Varus by night with the rank of envoys…

Or Nepos, Datames:
Pari se virtute postea praebuit
With equal himself courage afterwards he offered.
i.e., He offered himself with equal courage…

In some ways it’s the second pattern of syntax that is trickier, since it is even more at odds with English word order. Of course if you know the grammar and vocabulary, you can piece it together from the parts. But presumably that’s not how the author intended these phrases to be dealt with by a reader. Any tips on effective ways of adapting an English reader’s mind to this sort of syntax, so that these phrases seem natural?

looking for interlinear of Caesar's Gallic War for Kindle
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legatorum numero – “in the capacity of envoys” or just “as envoys”.

Pari se virtute postea praebuit – “Afterwards he showed himself [to be] of equal courage” (with his deceased father).

Update: I intended to update this post when I got the time, but mwh has written everything I would have written–and better, too.

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Not much in common between these two apart from the word order not coinciding with English. So I guess the most important thing for readers to get into their heads is that Latin word order is not English word order. It hardly requires a “strategy” to impart that understanding. Mere exposure to real Latin should be enough.

In the Caesar, missis should set up the expectation of an abl.absolute, an expectation confirmed by centurionibus. And the reader should realize that everything sandwiched inbetween is part of that. The abl.abs. can be commaed off or parenthesized. A hierarchical parsing diagram might be useful.
In other words, reader should learn to analyze as missis … centurionibus, “there-having-been-sent (to-V, by-night, as-envoys) centurions.” And if translating should learn to turn this into English-sounding and context-sensitive English.

In the Nepos, it’s only the position of se that might throw a reader off. So reader should learn that second position (in sentence or phrase) is normal for unemphatic personal pronouns. To help this sink in, you can expound Wackernagel’s Law.

My tip for making such phrases seem natural: when reading Latin, do not translate. Get English out of your head.