Thank you all for the input. I had pretty much discounted natural carbonation for the reasons stated (but, I didn't want to think I might have missed something), and bottle bombs are just not something I really want to deal with. My hubby has a couple of corny kegs, both 5 gallon and 2.5 gallon, and I'm sure I could wheedle him into letting me make the attempt with at least a 2.5 gallon. My current 10 gallon batch of Joe's should give me enough to play with.
Other than my first batch (I'm on my 4th now), I've never had anyone comment on any pithyness in the taste. I don't juice the oranges first, but I do trim out the excess pith at the ends of the slices as well as any of the stuff that 'strings out' from the middle of the slices. I also cut them into slices small enough that I'm not having to smash them too terribly much to get them in the carboy. The only reason for the smaller slices is because I hated the juice going over the outside of the carboy as I smooshed them in and cleaning up the mess. I also add enough water to be able to dissolve the honey using a lees stirrer and a drill before I add the rest of the ingredients, and then give it a more gentle stirring after everything is in by hand with the lees stirrer. The other thing I do is make sure that I get the oranges as ripe as I can. I've used three different kinds of oranges so far; Navels, Valencias, and Cara Cara, and it was the Navels I used n my first batch and were the ones that gave off the pithyness. But, that was also my first batch, and I followed the directions exactly, including how small to cut the oranges. I didn't want to void the warranty. ;D