That period had one distinct #1 and one distinct #2 - Bradman and Headley respectively....all the rest take a backseat to these two....
Headley was undisputed #2 ? Don't believe the numbers (and CLR James) blindly
Check the series averages of Headley before the war:
1929-30 : 703 at 87.87 v Eng
Bowlers : Voce (20 year old debutant), Nigel Haig, 52 year old Rhodes, Greville Stevens, Jack O'Connor, Ewart Astill, Len Townsend
1933 : 227 at 55 v Eng
Bowlers : George Macaulay, Gubby Allen, Verity, Walter Robins, James Langridge and 'Father' Marriot. When Headley score his only 100 of the series the attack was Nobby Clark, Macaulay, Robins, Verity and Langridge
1934/5 : 485 at 97 v Eng
Bowlers : Jim Smith, Bob Wyatt, Eric Hollies, Some Paine, and Ken Farnes
1939 : 334 at 66 v Eng
Bowlers : Bill Bowes, Bill Copson, Doug Wright, Headley Verity, Tom Goddard, Morris Nichols, Reg PErks
In his 14 test against England, the England first XI bowlers that he faced were Farnes (2 tests), Verity (3) , Allen (1), Wright (3) and Bowes(2) who was past his prime. No wonder he scored heavily.
Australia fielded their full strength side against West Indies. They weren't all that strong themselves beyond Grimmett. O'Reilly did not play in any Test. And Headley scored 336 in 5 tests at 37. This was probably more like his real average.