While reading this I happened to have Brian Haresnape's book "Railway Liveries 1923-1947" on my desk to check something else.
On page 114 he states that from 1928 to 1939, the second period, the number of locomotives using crimson lake was now restricted to the more important and modern. i.e: 4-6-2s, Royal Scots, Jubilees, Claughtons, Hughes 4-6-0s and 4-4-0 compounds. This is the period with "LMS" on the tender.
They were of course crimson lake prior to 1928 with the loco number on the tender.
From 1939 onwards any repaints were black.
David
Edited, as usual, to correct my poor typing.