Just ask. You can use your other job as leverage.

The fact is, you specifically say that you "feel I need the internship experience to make transitioning out of school into a web dev position easier."

Considering this is your only offer (I assume), you don't have a ton of leverage for getting more money.

As for logistics, email or phone is fine. In-person is just awkward for what amounts to a 5-minute phone call. They'll be back and forth on their end.