When I'm desperate, I send my customer a Paypal invoice referring to the eBay transaction number and explaining why I'm using that system.
The buyer is covered by Paypal's Buyer Protection which is perhaps a little stronger than eBay's. Which I also explain.
And of course, when he pays, I just mark it Paid manually as if he had given me a money order or cash.
There may be a more official way, of course.