There are a lot of urban legends out there to be careful about. Almost every station that dates back to the 1920s or 1930s but didn't end up with a clear-channel signal now tells a story about how "it was offered a bigger signal, but the owner couldn't afford the transmitter" or what have you. Those stories are, for the most part, excuses made up after the fact. The stations that did upgrade in the 1940s weren't "offered" bigger facilities. They lobbied hard for them, often using political connections or affiliations with powerful newspaper ownership to get them.
It's not hard at all to track the biggest of the frequency shifts. On March 29, 1941, nearly all AM stations on the air in the US and Canada changed frequency, and most of them did so according to a very well-defined pattern. Hit up the 1941 and 1942 Broadcasting Yearbooks at
www.americanradiohistory.com and you can follow the moves. In a nutshell, everything on 720 and below (WSM, for instance) stayed put, while nearly everything on 740 and above moved up either 10, 20 or 30 kHz.
The "graveyard" channels moved en masse: stations that were on 1200, 1210, 1310, 1370, 1420 and 1500 moved to their now-familiar homes on 1230, 1240, 1340, 1400, 1450 and 1490. Some of those stations were then able to move again to better regional channels later in the 1940s.
Here's the Broadcasting Yearbook section that outlines the 1941 shifts:
http://americanradiohistory.com/Archive-BC-YB/1941/NARBA-BC-YB-1941.pdf