In case others need the help, my problem was due to having logged into Stardock with one email, and then purchasing the products with a PayPal account under a different email. You should be sure to use the same email for both.
This is an unrealistic request, given that Paypal can have many email addresses tagged onto the same account. Mine has three - my business email (the primary), my personal email, and my gaming email. I can login to Paypal using any of them to manage the account and/or make purchases. A purchaser should not be limited to the primary email on their Paypal account when registering a Stardock account (or with any online retailer for that matter). The purchase system Stardock uses should be smart enough to tag the account logged in at the time of purchase with the correct transaction ID from Paypal. If it doesn't or cannot, it is either broken or incomplete as a digital storefront.
The reason I'm pointing this out: I just spent over a week (8 days total) waiting on 2 replies from Stardock support, to try and find out what happened to old keys I bought out here. Then after sorting that out, I purchase an upgrade to Object Desktop... and ~4 hours later there's still no download link / key in the Downloads area.
From what I can see, the entire Stardock storefront needs an overhaul, or needs to quit using Paypal until it works properly.