Conclusion: eBay will allow you to use your PayPal account as a reimbursement payment method if you call and complain (and tell them that you don't even have a credit card number to give them, which is true in my case.)
Does ebay have a method of tracking completed sales which are not followed by a paypal payment? If they require paypal, surely they must see if no paypal payment has been made. Would they come down on the seller in this type of case?