Kurt and Tommy Godwin will probably have beaten 10000k in a month, and Steve as well, I would guess, as incidentals in their quest for the year record. I reckon Kurt's 15/11/2015-15/12/2015 would be well up there. He was over a Godwin for every day that month.
15/11 to 15/12 for Kurt was 6954.8 miles (11192.7km).
Kurt's best 31 days was 6983.3 miles (11238.5km) at day 165, so that's 25/6 to 25/7 inclusive as June only has 30 days).
Kurt's best calendar month was July 2015 with 6883.1 miles (11077.3km)
Steve's Best 31 days:
Attempt 1: 6866.7 miles (11050.9km) from 10/6 to 10/7 (inclusive)
Attempt 2: 6638.7 miles (10684.0km) from 15/8 to 15/9 (inclusive)
Steve's Best calendar month (it's the best result from either attempt as it is common to both):
6469.6 miles (10411.8km) in October
Tommy's best 31 days was 8773 miles (14118.8km) from 21/6 to 21/7 (inclusive)
Tommy's best calendar month was July 1939 with 8583 miles (13813km)