In this particular case (i.e. not eligible for TWOV), the exchange student definitely needs a visa. But, since the work permit isn't going to happen, I'm wondering what other sort of documentation could work.
[MENTION=10058432]matthiasride[/MENTION]
a few more thoughts:
-try calling one of the visa agencies listed here (or searchable via google), and explain your situation to them; they charge around $100 if you engage them, but the phone call is free
-if it were me, I would visit the DC consulate in person on a Tuesday morning with all of my ducks in order (passport, student ID card, extra passport photos, completed/signed application, dummy airplane reservation, and dummy hotel booking...the more, the better)
-another option is to send the passport to Pakistan in order to apply there
Feel free to privately message me any time.