What I would do is double the number of cast-on stitches, putting a marker at the beginning of the round and halfway around. Usually you leave out the very edge stitches when you convert a pattern to account for the stitches that would be seamed, but it might be easier with all the decreases to leave them in. It would only be a 4-stitch difference.
Work each section between the markers as if they were the front and back that you were knitting separately, and when you get to the armholes, work them back and forth as if you'd been working the pattern flat all along.
Of course you'd knit every row in the round to get stockinette stitch.