I see, yes being in the round and probably not that large a diameter makes it feel crowded. I think your idea of putting all the sts onto a single needle would work. What about onto a circular needle if you have one? It can be longer length and it can be a smaller needle size than the project needles because you're just knitting off it like a stitch holder. (I didn't mean that you should go out and buy a st holder btw, I mentioned it in case that's what you were using.)
The other thing you could do is put most of the sts on some scrap yarn and only put one dpn's worth on a needle. Work the sts together to the end of the needle and then load more hem sts onto the needle.
It's a nice technique but a bit more of an engineering problem in your case!