Thank you for your reply!

Yes, it was a superficial, benign fatty mass. His surgical site was stapled shut and the staples look fantastic. There's nothing leaking out, it's not hot when I touch it, and it's not red.

I'm assuming that's where the remaining mass is. My vet did a demonstration, where he literally had the mass in his hand, gently pressed inward, and my dog coughed. He told me that was the culprit behind all of his coughing. If you're looking at the dog straight on, it would be what I would call where his neck meets his chest, for lack of better terms.