With my fly rods, I have to move the rod a bit faster when casting a faster action rod than one with a more slower moderate action.

But in spinning rods of the same length and line/lure weight, wouldn't I have to exert a more crisp cast with a faster action rod to cast the same 3/8oz lure than I would if I were casting a much slower action? Seems like the more moderate action would load further down the blank creating a longer radius to launch the lure the same distance with less effort than a faster action - yeah or nay?

I think that it's how FAST it moves, not how far. Tip velocity determines the initial velocity of the lure.
At least that's what I would think from what I remember from physics.

How far or how deeply a rod loads will also have to do with the power it has, no just the action

The greater the velocity for the same trajectory the farther the lure should go.

........

Tim,
You are basically correct. How much force you apply and how rapidly you apply that force will determine how much energy is stored up in the rod. How rapidly the stored energy is released is a function of the rods resonant frequency. All other things being equal, i.e. length, power, material, a faster action rod will have a higher resonant frequency than a slower action rod so it will require a faster casting motion.
You are also correct that, all other things being equal, a slower action rod will store energy in a larger portion of the rod than a faster action rod but will then take longer to release that stored energy so require a slower casting motion.