Just as many people felt Indy didn't fit in the 1950s, I don't feel he fits in the 1940s. 1940s = film noir for me. Indiana Jones isn't film noir. The late '50s-early '60s period at least works in a sense because that period isn't not really associated with any singular genre. But seeing Ford (or a replacement actor) in say, 1943, try to be Bogart wouldn't work for me.
The only way a post 1939 period works for Indy is if you ignore the world at large. KOTCS hammered that we were in the 'nifty '50s' in our faces many times throughout the film when it didn't need to. It only deepend the divide between it and the existing films. And if you make a film set in the 1940s, which also ignores the 40s, what's the point of setting it then in the first place?
I view WWII as the start of the modern era. The age of the Atom. Indy was supposed to harken back to a time when the world seemed to be a much smaller place. There's a reason none of the original trilogy is set during the '40s.
And the Nazis have really been done to death as villains, both in pop culture and in Indy too. They no longer have the scary, spooky effect they once had. They're overplayed.
It's too bad KOTCS was set so late in the 50s. Seeing Indy around the time of the Korean War, in Asia, with vicious Chi-coms or Korean Communists as the enemies, could've been interesting. Some of the most brutal, bitter fighting was at Chosin in frozen Winter.