I realize this question is very old. I'm answering anyway, as this is a thing that people commonly want to do!
I'm about to build a water pipe shelving unit that features several closed rectangles. Since this will be a decorative item, I want to use the malleable black iron fittings (like you have), and not the "structural" fittings that appear in one of the other answers.
As you've figured out, you cannot screw together a closed loop made entirely from right-handed threads. To solve this problem, I'm simply going to cheat: I'm going to grind off the threads on one end of one of my pipes. They will be ground down to where I can just press the pipe directly into the fitting without screwing it in. Then, I will screw together all the other fittings, and gently flex the parts to push-fit the final fitting. Finally, I'll make it permanent by tack welding the fitting in an inconspicuous spot.
If you don't want to permanently assemble the parts, you could drill and tap a hole in the junction, and use a set screw to hold the fitting together.
The main challenge is grinding down the threads in a way that still looks good, and not obvious. I have a metal lathe that I will use for this (cheating!), but a more modestly equipped workshop could use a hand drill to rotate the pipe, and an angle grinder, sander, or a file to grind down the threads as the pipe is spinning.
The main challenge would be chucking the pipe into the drill, since it's too large for the chuck to grab it directly. Consider making a jig by buying a threaded end cap that fits over the end of the pipe, and drilling a smaller hole in the center of that cap. Then, you can secure a hex head bolt into the hole using a couple of nuts, and then chuck the bolt head into the drill.
To keep the other end of the pipe from flopping around, you'll want to use something to stabilize it. A cone-shaped mandrel, or a pipe that neatly fits inside the pipe being worked on would work. These could be secured in a bench vise or such. Alternatively, a loose fitting sleeve on the outside of the pipe (such as a coupler or another piece of pipe) would allow you to apply lateral pressure to the pipe so that you could hold the threads against a sander or grinder.