There's a neat trick where you can make yourself eligible online. I just did it so I'm ready to pre-order on Saturday at 2 am central time.
Go into your account online and go to upgrade the line you say has one payment left. Go through the whole process of saying you want to upgrade and will pay the $X amount to be eligible for a trade-in upgrade (this means choosing the new phone you want to "upgrade" to. I chose the 6+ it doesn't matter because you're not actually going to upgrade, just pay to be eligible).
You'll come to a page where you first have to pay the remaining amount to upgrade separately. Make that payment and then cancel out of the potential upgrade...wait a minute and then go back into the main page of your account. That line should show as eligible for upgrade.
You're ready to pre-order.
I tried the AT&T chat function, but the guy had no idea what I was talking about when I asked if I could pay the remaining amount ($42) in order to be eligible to pre-order the new 6s+.