Here is a link to the mittens from Ravelry. LINK
They are gorgeous!!
Carrying the main color behind the alternate is pretty easy; but carrying the alternate color is ... ... I bring the yarn from right to left behind the needles, hold it down and make the stitch with the main color & take the alt.color back, every other stitch. Of course, the alt.color yarn likes to fall off my right index finger when I do this.
Since you are working in the round this is pretty easy. I'm not sure what you are doing. I work this way, one color in each hand a lot and I just keep both colors behind the needles all the time knitting with one and then the other as needed. Are you trying to catch things down with every stitch? I guess some people like this idea but I don't. I would just carry the unused yarn loosely across the back accomplished by spacing the stitches out across the right hand needle when you change colors and take the first stitch with a new color. You don't even have to do that if you are only doing k1MC, k1CC or even k2MC, K2 CC doesn't take much attention. If you have to go more that 5 stitches between color changes, which it doesn't look like you will have to do very often, that is the only place I would catch in the colors to keep the floats from getting too long. Stagger them so that the places you catch in are not right above each other round to round and they will not show up much.
I notice I'm keeping the right hand yarn above the left hand yarn, but no extra hands or fingers needed to hold anything down or anything.
Catching things in every other stitch is not necessary and IMO not even a good idea. It makes the mitts less stretchy and not really any warmer and you are not going to be catching your fingers on strands that are only 5 stitches long with Palette yarn. Good luck with your beautiful mitts.