Why is it that when my chain is really tight, and I spin my wheel, the cranks don't move? But when I put slack in the chain and spin the wheel, the cranks start to turn.

It seems that the opposite would be true.

this is by no means a well educated guess, but just a hypothosis... maybe when the chain is really tight it's putting a little pressure on the bearings in the BB and so it's not as free to spin on a whim?

That, coupled with a cheap Dicta cog might just explain it. It makes perfect sense.

one word --> friction