I think your daughter just posted the question, but here's a little trick I learned as a PAO in the Coast Guard, while trying to coordinate with other services.
With listed phone numbers you'll recognize a pattern....
General Line: 860-555-1120
Person 1: 860-555-1122
Person 2: 860-555-1123
Person 3: 860-555-1124
Person 4: 860-555-1125
Person 5: 860-555-1127
Those numbers are related and listed. The general number is likely a receptionist. The others are, in this case, admissions officers. I'd look at the listing, and after getting no responses from those numbers, try the numbers missing that aren't listed.... maybe 1121 or 1126.... of bookend it, try 1119 or 1128.
The other thing you can try is calling a known number, maybe the cadet watch office, and asking for the direct number for a specific person. Direct numbers aren't protected in the federal government.... all you have to do is know who you're looking for and ask.
Now let's say you get one person who doesn't work on your application package, but you can't get anyone else. You can call that person back, explain the time crunch and the issue and often the person can "walk it" to the correct desk.