My 813K looks exactly the same from the front and profile views. It has the same individually lit dial glasses for the bands, the same motor drive and "Magic Brain" station preset system, and the same ever shrinking tenite escutcheon. Same knobs and curved dial glass.
I'd say that if the cabinet is in good condition, I'd go as high as $200 for another 813K.
It's a pretty extensive job replacing all the rubber wire, and there are a boat load of caps that will need updating. The controls switches are tough to clean, and the tuner gears, linkages and motor demand a good bit of time too. Oh, and don't forget the spider web of a dial cord.
Add on the work involved in an alignment, and you've got a pretty involved project on your hands.
I don't think I'd even look twice at one that needs cabinet work. You'd be better off to built the whole thing from scratch.