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Chris,
First of all, you never want to install ducts in a slab on grade or below a slab on grade. This is an old, discredited approach. Many such duct systems developed moisture problems and mold, and had to be abandoned.
Second: I don't recommend the perimeter loop approach. Modern duct systems should be as compact as possible. Longer duct runs require more blower energy than short duct runs. In an energy-efficient house with high-performance windows, it is usually possible to locate the supply registers near the center of the house rather than at the home's perimeter (because good windows don't cause winter chilling like the leaky windows of old). If you are able to do this, your duct runs will be short -- making your distribution system more efficient.
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Just as a quick add to Martin's bit about efficiency in duct runs, picking efficient fittings is far more important than keeping your duct runs short by locating them in the center. That might save you 20' but if you pick lousy fittings, they can have effective lengths of 50' or more! That adds up real quick. They will erase savings from keeping your duct runs short quick. Combine both of the those, short runs and good fittings and you'll make a good hvac man weep for joy.
Also, when you live in a heating dominated climate (I'm guessing you don't, since you described your unit in tons) then you usually have floor outlets. These typically go to the outside under windows because that's where you have floor space for them that won't be covered by furniture.
Even at 32F outside, you can still get noticeably uncomfortable drafts near windows that would be reduced some by under-window registers.
Possibly some type of perimeter design could make use of space provided by a tray ceiling. Extra length can always be compensated for with increased size.
I find the radiant effect of hot air ducts significant. Ie, a duct running under the floor heats the floor and sitting above it is noticeably more comfortable.