Talk to the teachers again. It's likely that he really truly is fine -- he is crying as he transitions away from you but once he's there and engaged, he's part of the group. Ask the teachers more specifically how and what he does once you leave.
Is there a way you can drop in during the middle of the day and observe him, but he cannot see you? You might be surprised to see him playing and participating with not one tear.
And be sure that your drop-offs are quick and firm --it sounds like they are already -- just be sure you don't go back for that extra hug or linger just a moment while he cries for you in his teacher's arms, etc. That only prolongs his distress and sends a signal that you don't quite trust his being there and are hesitant -- he needs to see that Mommy is comfortable with his being there and he'll get more comfortable too.
Some kids, though not all, do go through a clingy stage around 3 when left in day care or preschool or health club kids' rooms, etc., even kids who are outgoing and not clingy at home or with adult friends of yours around. It seems pretty typical. If you send him to a home day care again where he's the sole kid again, or one of very few, he'd have to make yet another transition, so give this one a chance. I've seen kids dropped at preschool who were distressed every morning for quite a long time but who by the year's end were doing fine. It's a tough age -- for both of you. Make the teachers your allies in this because they've handled it all.