I recently spoke with apple support about this because I am in a similar situation of wanting to join the IUP and trade in my non IUP iPhone that I own outright. I was told you sign up for IUP as usual and pay the regular quoted rate. You can bring your old phone to apple store and they will issue a credit to your credit card for the trade in value. You cannot apply that as a down payment to reduce your monthly IUP bill.
i personally will go to the apple store and do the trade in in person bc i have had a bad experience with mailing in a device and the service center lying about condition and reducing my payment. Just my opinion for that. I do not know how it works if you mail your phone to apple for the credit to your card vs a gift card.