I see no one has mentioned this so I will -

The "James James" poem is "James James Morrison Morrison" I believe (James James Morrison Morrison Weatherbee George Dubree, took great care of his mother though he was only three")

The Chad Mitchell Trio recorded a setting of this poem ('way back in the vinyl days) perhaps on "Typical American Boys" perhaps not. I think the setting was Mitchell's, but not sure about that at all.

It's the only Milne piece I know of. (The Kenny Loggins tune is, I think "House at Pooh Corner")