If you paid for the items, they aren't taking a loss. Seems like with your "proof", they could go through their automated (?) system and find your purchase, and confirm the items you purchased, and give them to you.
I'd get credit card company to send me a copy of whatever info they have about the transaction, and go back to see the manager.
All I know is what various retailers I've worked for would do. Target would go on the electronic journal on the computer, enter your credit card number in the search function, find the transaction (including time), check the video, say "aha; there he his leaving the chairs", hand you the chairs and apologize for the delay. Home Depot would tell you tough shit. Safeway would apologize profusely for distracting you and causing you to forget the chairs, toss in another chair to make it up to you, and thank you for your business, all before realizing that they don't even sell chairs...
As far as the chairs ending up in the "paid for and left behind" area, it probably didn't happen at selfcheckout If the person watching selfcheckout wasn't alert enough to notice you leaving them behind, they'd have no idea whether or not they were paid for and would just assume someone changed their mind and left them.