[Flibmeister]

Okay, I've found the answer to my own question, and it should help others with the same problem-- it seems silly, but it works:

If you want to keep the screen from going black immediately after call connection, don't immediately put the phone up to your head after dialing. Instead, hold it face-up and flat after dialing-- the screen stays lit. After five or ten seconds, you can move it to your head and it will stay lit during the call.