After 13 Navy moves, here are my two cents:
Realize your stuff is just stuff. Sometimes very nice stuff, but still stuff. Insure it if you want and make a claim when something does get damaged or lost - of course it will happen. Surprise, no one cares as much about your stuff as you - not even when they're paid to. (Except maybe the Japanese, man those guys were enthusiastic!) It's not worth losing sleep over or losing your cool on.
I used the Navy picked movers for all but 2 mid-tour moves. Some were good, some were not. The gouge presented about being friendly, providing food and drinks (++ for asking what they would like prior), and paying attention to the packers and inventory are all spot on.
The Navy won't foot the bill for mid-tour moves except under certain circumstances. On one of two mid-tour moves I packed and moved all the little things and hired "Two Guys and a Truck" for the monster items. On another one, I and a bud in the same command swapped labor for each other's mid-tour moves. Both those were on my dime.
As far as DITY and making money: yeah, you can, but are you and your buds in the moving business? I never needed the money bad enough to put someone out that bad.