Believe me, you're not the only person challenged by this concept. We've almost all had the same or similar questions and gotten help over them so you might as well benefit from our collective experience.
You don't have to transfer the stitches and in fact you couldn't put these sts onto one straight needle. When you get to the area of the thumbhole, turn your work as you would if you were at the end of a row. That means you'll take the right needle in your left hand and pick up the former left needle with your right hand and start purling. The purl side is the WS for this mitt.
When you've purled around to the thumbhole (a slight opening at this point), turn again and start with knit sts on the RS.
Good luck finishing these very good looking mitts!