After reading this thread, I sent off an e-mail to the "upgrade" address this morning. Not knowing when I may, or may not, hear back from Sprint I then decided to send another e-mail to the "Sprint Cares" address. No longer than an hour passed and I received a reply from the "Sprint Cares" address just asking for my account PIN so that they could access my account and look into the upgrade. After another hour or so passed, I received an e-mail back saying that I was getting the upgrade.
So, the moral of the story is that by using the original e-mail address for customer service I was able to take care of the situation within hours instead of waiting on some kind of a response for a new address that may, or may not, yield results.
By the way, I wasn't due for my upgrade for another year.