I managed to get it to work. Here's what I did.
1. From the PayPal transaction import screen, I imported the transaction to my register and when asked if it should be classified as a Sales Receipt, Invoice, or Deposit, I chose Deposit and added it to my register, selecting the correct Customer name below.
2. Because the invoice was for a specific Project, I needed to then go in and edit that deposit to change the payer from just the Customer to the Customer : Project.

3. Now I was able to go into the Invoice and select Receive Payment. On this screen, I was able to associate the newly created deposit.