C/E didn't sound quite so good to me, but I think it depends on the style. It's almost the same as Am/E so it would definitely work - maybe you're getting a better inversion.

As for D instead of Dm - it seems to me that D is a little more interesting. D is the "V of V" chord in C - in other words D is the V chord in G major and G is the V in C major, so there's definitely a case for using it.

It also adds a little tension because of the F# in the D chord moving to the F (natural) in the F chord.

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