Viscount, good information…if I can add a bit to corroborate your post.
Yes, you’re correct about big props in use. As I mentioned above, when I flew to Japan in 1961 we flew in a DC-6 owned by “Twentieth Century airlines”.If one looks very closely you can see mentions of it in various lists of charter lines. It was small, I believe the senior flight attendant on our flight was married to the captain!

Yes, piston were being relegated to smaller routes and carriers, but remember that the newest DC-6 was built in 1958 and the type would see service on U.S. domestic routes with major carriers for quite some time. For example, United flew them into (circa) 1966 when they were finally replaced by 727s.

When we returned to the USA in the spring of 1963, it was on a chartered Pan Am 707 flight. Compared to the three day piston flight which required stops in Honolulu and Wake Island, the jet flight seemed like a spaceship. aside from the obvious doors advantage, I recall that unlike the Douglas, the 707 flew so high that you didn’t see the waves for hours on end. Sadly, a stop at Wake was no longer required.