As frustrating as this must be for OP, what proof does he have? Any Sony chat logs or information on registered serial numbers means nothing - if the buyer ships back a different serial number and claims that is what OP sent, how can OP prove otherwise? All that Sony info just shows that OP had a PS4 with that serial number at some point, it can't prove he posted it to the buyer
Frankly at this point eBay needs some kind of physical escrow system for higher value items. You ship your product to eBay and they verify it, then ship it on when payment is received.
The proof is his account info, address, name, etc should be the same on PSN and eBay. With that info Sony can show what systems he used, if they were banned, their serials, etc. If the OP gets the old broken PS4 back without matching serial number, eBay can cross-reference his personal info with Sony.
The problem isn't what proof he has, the problem is that eBay won't waste that much time doing any of that.
I still feel had OP got out ahead of this with eBay and cut off all contact with the buyer he'd be in a better place. The OP didn't and chose to deal directly with the buyer instead with threats.
If all we have is the timeline of events the OP ran through in this entire thread as a base, the buyer's claim and the OPs responses NOT including any other info shared here about the story but JUST correspondence with eBay and the buyer, I'd side with the buyer, too.
Still, OP needs to escalate over the PHONE and give them all the info he has, not open any box from the buyer and contact the BBB. That's about all he can do right now.