If buyer is asking for a delivery timeframe that even your listing’s EDD does not indicate as possible, they are asking for something not in the scope of the purchase. 

The request/command to communicate by email rather than through eBay messages is weird given that eBay friend on such communications. How did their written email address even make it through the message system?

I wouldn’t call the message “rude”, but it does express expectations that are not what you say you promised in the listing. “Demanding” tone, yes

Based on the information you’ve provided, I’d suggest cancelling and refunding with “Problem with buyer’s address” as the reason, given that you couldn’t get the urgently desired poster to their address in time as they expect.