But this process, including sending smaller items first etc sounds like it would have taken longer than what the OP did? And the OP was trying to do it quickly to tie in with the beginning of the semester?
Forwarders work with batches: small batches (consolidate packages in a suitcase to travel as airline luggage) or large batches (up to a whole 40 feet container)... So, delay is a matter of luck - ask around if a batch is due to depart and available slots remain. Express remains the province of traditional players - though I've managed to find a forwarder to urgently ship a small blister of drugs, but such service isn't guaranteed.