I figured it out after chatting with an Apple rep on iMessage:
“With trading in online, since we have a financing plan that allows the value of the trade-in to lower the monthly payments and is able to be applied immediately, before sending in the trade-in, the iPhone Upgrade Program option does go away when adding the trade-in. The options available are the iPhone Payments and full price purchase.”
“With the trade-in and iPhone Upgrade Program enrollment, once the credit for the trade-in is applied to the taxes and other items on the purchase, the remainder of the trade-in value would be in the form of an Apple Store Gift Card. With our financing partner, Citizens One, they have provided the iPhone Payments plan as an option to apply the trade-in value to lower the monthly payments, but with the iPhone Upgrade Program, that option is not there as they have the pricing set with the AppleCare+ included in the monthly payment, which we are not able to adjust I’m afraid.”
I was really after iUP, but at this point, since I’m already pre-approved for AIP, going to stick with it. It’s the most efficient way at this point. Plus I’m getting full trade-in value for my X and not a gift card, which is good.