You're talking about the third match of the recent series, in Bristol, which sadly was rained off with England looking set for a monster total after reaching 280 for 4 in 31 overs.
This list is still led by Sachin Tendulkar, who piled up 673 runs in the 2003 World Cup. Matthew Hayden came close with 659 at the next one, in 2007. Three men topped 600 at the most recent World Cup, in England in 2019 - Rohit Sharma scored 648, with a record five centuries, David Warner 647, and Shakib Al Hasan 606.
It's not quite right, if you stick to the exact wording of the question. Graeme Hick is the last man to score 1000 first-class runs in an English season before the end of May in 1988, but 410 of his runs came in April. The only men to score 1000 or more entirely in May are WG Grace in 1895, when he was 46, Wally Hammond in 1927, and the Lancashire left-hander Charlie Hallows in 1928.
Two men lead the way in this mournful list with five ducks in World Cup matches: Nathan Astle of New Zealand, and Pakistan's Ijaz Ahmed. Astle did make two World Cup hundreds, while Ijaz ended up with a winner's medal in 1992, so it wasn't all bad news for them.
This question came about when you spotted that the website's list of the highest run-aggregates in ODIs, which goes down to 650, did not include any matches in which both sides lost ten wickets. But the highest in which 20 wickets went down just misses that list: there were 642 runs in a 2016-17 match in Greater Noida, when Afghanistan were all out for 338 off the last ball of their innings, and Ireland replied with 304 in 47.3 overs.
Steven Lynch is the editor of the updated edition of Wisden on the Ashes