Well, DH and I talked things over again tonight. I don't think it'll change the neighbors' opinion one iota, but I think we're going to cut down the height of the shed. We think we can shrink it 1.5 - 2', yet still keep 6' walls. Sure, we'll have to duck in the door, but I can live with that. It will make the scale of the shed more in line with that space.
I think that's a compromise I can live with. I am doing this for ME, and my own peace of mind. I know nothing will change the neighbors' opinion other than tearing the thing down, and I don't believe they have the right to tell us we can't have a shed at all. I am willing to do what I can to minimize what they see while still keeping it useful for us. If we cut down the height, that would leave maybe 2' - 3' visible over their fence -- way less than if we had put a play fort over there. At that point, I will feel like I made a fair effort to balance their property rights with mine. Again, if they were so concerned about what they saw from their pool, they should NOT have erected a see-through, 6' fence. They needed to put in an 8', board-on-board fence instead. This is small-lot surburbia, after all.

You never know what nosy neighbors you might have.
Thanks again to everyone who shared their thoughts and opinions. It really was helpful for me to gain perspective from both my neighbors' point of view as well as mine.