I haven't built the kit, but I can offer some generalized suggestions based on "prototype practice."
When the sails were furled the skysail, royal, topgallant, and upper topsail yards were lowered until the standing lifts (the wire lines running from the ends of the yards to the masts above) were taut; the lifts supported the weight of the yards. That put the topgallant yard a couple of feet above the topmast cap, and the skysail and royal yards a foot or a foot and a half above the bands where the heads of the topgallant and royal stays, respectively, were secured.
Photos of latter-day, double-topsail-rigged sailing ships often show their upper topsail yards lowered almost on top of the lower topsail yards (which were permanently mounted to the lower mast caps, and didn't move up and down as the sails were set and furled). But there seems to have been a custom that the crack tea clippers maintained a bigger space between the topsail yards, for the sake of appearance. Mr. Campbell's plans show about 10' 8" separating the fore and main topsail yards, and about 9' on the mizzen.
The studding sail booms would only be run out when the studding sails themselves were set; otherwise they'd be slid inboard until they projected only three or four feet beyond the ends of the yards. I haven't seen how the boom irons of the Academy kit are made, but the real things are fairly simple. An studding sail boom iron essentially consists of two iron bands, connected by a short iron rod (the rod is just a few inches long). The larger band runs around the yard; the studding sail boom slides through the other one. (The band through which the boom slides may be made in two pieces, connected by a hinge.) The outer boom iron consists of an iron band for the boom to slide through, with a forged iron bracket welded to it. The bracket is made in such a way that it slides over the end of the yard; there were variations on that theme, but in the Cutty Sark's case the bracket is an elongated U-shape, with holes in it for nails that fasten it to the yard on the fore and aft sides. Mr. Campbell's book, China Tea Clippers, contains (p. 120) a nice set of drawings that shows all this in detail.
Mr. Campbell notes that the Cutty Sark was somewhat unusual in carrying her lower studding sail booms below, rather than above, the yards. (The booms on the upper topsail yards are in the conventional positions, above the yards - as are the ones on the main topgallant yard.)
I'd have to take a look at the kit to form a firm opinion of how best to represent the studding sail boom irons, but when I've done it I've made them from brass tubing and wire. The inner iron can consist of two slivers of tubing connected by a short piece of wire. The following is an easy sequence for making them: 1. Drill holes in two pieces of tubing to fit the wire. 2. Cut the tubing on either side of the hole, about 3/16" long. 3. Cut a piece of wire to a handy length and pass it through both holes. 3. Pin the pieces of tubing down to a fireproof surface, so they're in line with each other and the right distance apart. 4. Solder the wire to the tubing. 5. Trim the wire to length and file the pieces of tubing down to the right thickness.
The outer boom iron, on such a small scale, can be a slice of tubing with a piece of wire soldered to it; the wire can just be plugged into a hole at the end of the yard.
If Academy has rendered the bands on the yard pretty well (as I suspect is the case), half the work has been done for you. Just drill holes in the plastic bands at the right places, and plug the wires on the new bands into them. The boom irons should be angled 45 degrees below the horizontal on the lower yards, and 45 degrees above the horizontal on the others.
I suppose it would be possible to use styrene tubing instead of brass, but the styrene tubing I've seen has awfully thick walls. Brass is nice stuff to work with, and decent hobby shops stock it in a wide variety of sizes. Look for "telescoping brass tubing" in the K&S Metals rack.
Hope that helps a little. Good luck.