Hi, it's a pleasure to have you in the Community today. I've got you covered, and let's work this out so you can complete your tasks in QuickBooks Desktop (QBDT).

Before we do so, can you tell me more about your concern? Are you trying to process customer payments? What are you trying to do when you say "attach a payment to a customer account and then use that deposit on the account towards an invoice while also keeping a reference to the order in which the deposit is intended to be applied?" This way, I can provide you with the most accurate resolution to your query.

You may also attach screenshots as well so we can have a better picture of your concern.

Additionally, I'm adding this article as your guide in recording customer transactions: Get started with customer transaction workflows in QuickBooks Desktop.

The Community is rooting for your reply. Take care and have a good one!