Daine,
How badly do you want to attend the "reach" school which just rejected you? We have a family friend in town who has a full blown college admission's advisory business. He said that it is not unheard of for an admissions department to change their minds--for instance if they didn't know said applicant is carrying a full tuition scholarship. If they do not know that fact then you should inform them. The battalion at that school may even be able to help you in that regard.
Sometimes schools reject an applicant because they don't really believe he/she will actually attend if accepted. This happened to DS #2 best friend. Accepted at Columbia, rejected out of state at U Mich. A low acceptance rate looks great in the headlines, but the holy grail in the admissions biz is high yield. Yield = how many you accept / how many actually enroll. Again, if you really want the "reach" school tell them.
You should also be honest with yourself and ask if you were rejected for a good reason. Were your numbers in the upper third of recent enrollees or were you truly "reaching". ROTC entails a huge time commitment. If you are a STEM major being graded on a curve you may be putting yourself under undue stress if you are not at the upper end academically in the first place.
If you choose to try and transfer, I can tell you that DS #1 successfully transferred AROTC 4yr scholarship from GA Tech (where he had been accepted) to Big 10 U. That, however, was 4 yrs ago and Big 10 U was $10k+/year cheaper. He followed the advice Clarkson just gave, but also enlisted the help of the admissions folks at the Big 10 U, who communicated with the battalion.
Best of luck!