I, too, wanted to get my orders ASAP. I wanted to move from school (and you need orders for that) and do my final required med school rotation at the site where I will be for residency. I thought that it would be helpful to get used to the system before I absolutely had to. I spoke to Ms. Cox and she told me that there was no one with whom I could speak to expedite the process. She told me that the best that they could do was to draft a kind of pre-orders orders, something that indicated what your orders would be, but unofficial. She stated that this MIGHT be available by the end of this month. However, when I spoke to the Transportation Office they stated that they needed official orders and that some unofficial orders wouldn't cut it.
Ms. Cox was able to give me the names of two possible contacts who may be responsible for issuing the orders. Unfortunately, I don't have those names with me. (they were only names anyway, no contact info). She indicated to me that there was really little that anyone could do to get their orders before mid-May (MID-MAY!).
Of all the branches the Army drags their heels the worst when it comes to the transition between medical school and residency. I have classmates in each of the other branches who are already making moving plans, while I am stuck waiting.
Hope this helps,
Geo
ps. never expect an email response from Ms. Cox unless it is to her benefit. Always call when there is the possibility that you can get her on the phone and she can't ignore you.