Follow Orders or Daven on Time? A Religious Conundrum

This month, two religious officer cadets were expelled from their course for failing to follow orders in order to daven on time. The case, which has garnered a small amount of attention in the religious press (link to Hebrew article here), raises a very interesting conundrum that religious soldiers must face as they serve in the IDF.
The facts of the story are pretty straightforward. The group of cadets spent a long night in a navigation exercise, returning to their barracks quite late at night. As opposed to the rest of their platoon, for whatever reason, three soldiers were not woken up at the proper normal time for davening. When they were finally woken up, they were already late for a scheduled lecture, and their commanding officer instructed them to enter the lecture without delay. When they protested that they had not yet davened shacharit (and if they waited until after the lecture, they'd miss the proper time for davening - z'man tefillah), the commander nonetheless instructed them to attend the lecture.
One of the soldiers followed the order and entered the lecture. Two others ignored the command and went to daven before entering the lecture. When the commanding officer of the officer training course heard about the case, he insisted that the cadets be thrown out of the course - which they were.
Now, the case has become something of an issue, especially after the army promised to make all proper accommodations for religious soldiers. Remember also that many of the best, most dedicated soldiers come from religious homes, so the army doesn't really want to antagonize the dati community.
After reading about the case on Shabbat, I asked my children: What would you do? Would you follow the order and miss z'man tefillah b'zmanah, or ignore the order and daven? Would it make a difference if the officer told you to violate Shabbat? Where does a soldier draw the line when he must choose between following orders and adhering to Jewish law? In an ideal world, he should not have to make that choice. But we don't live in an ideal world.
I've got my thoughts about the case, which I'll share in a later post. But it's a fascinating question to ponder.