Yeah twin standpipe should be completely silent. If it isn't, it just needs the ball valve adjusting.
The water level should sit either just below the level of the taller non-valved pipe, so the main pipe isn't taking down any air which makes it noisy, then if anything gets blocked at the ball valve, the water level will rise and the 2nd, taller non-valved pipe takes the excess flow.
Tanks with only one pipe can't restrict the flow as it risks a flood, so it takes down air which not only makes it noisy but causes salt spray in the cabinet which corrodes everything...
EDIT: Can't see any issues with the skimmer in the first chamber. If anything that's probably the best place for it. Should make access for cleaning easier too. It'd get in the way if you wanted to run filter socks though. Is that first chamber 11 inches? You'll probably have to build a little platform for the skimmer to sit on.