"Considering most buyers will have to ship the set, a grand or so would be a fairer price for an un-restored set."
A grand would be a fair price even if the seller lived next door.
Without any details of work performed/work needed, always expect a worst case scenario.
At $4,500, I would at least expect a YouTube video of them working. Like a full video with each appliance working from start to finish.
In the next year or so, I will be thinning the herd a bit and a complete breakdown of every single part replaced, work performed, and complete video of them running from start to finish will be posted before sale. Anything else is a scam, PERIOD!