I was using mine at about 3000ft two weeks ago and had a bit of a problem aquiring an initial signal when I turned it on. Once it was active, text messages were able to be sent but the timing became a bit dodgey. I got a load of messages at the same time a few minutes after landing which I should have got in the air. I didn't make any voice calls though. At lower levels of about 1500, it seems to work better in my experience. I don't know whether me keeping my phone on for the whole of the flight might have made things easier in terms of aquiring the initial signal.
I certainly wouldn't recommend using phone on a normal network. Seems a bit unreliable. Have you tried contacting the CAA (are you in the UK?) or the relavant people to ask for advice?
I doubt they would say yes, but if you asked a mobile network to set up a temporary transmitter for you and emphasise that its for a university, education, supporting the community (blah blah blah corporate responsibility crap), they might agree to help. I think they do this sort of thing for big events like concerts. You could ask them to point it towards the heavens and you might get a reliable signal. The baloon moving might be a problem though.