Thanks for that workaround tip!
Sellers who want to try that can edit each product and tick the box to Require buyer's shipping address in the product settings; if you don't see that while editing your product, make sure the box is ticked to Show Advanced Settings at the top of the product settings screen.
We infer this workaround means the problem may only affect transactions that do not require any shipping address, so we've added that to our ticket with PayPal MTS in hopes that may help them identify and resolve the reason for the problem.