Stripes in the round

Hi all! Working on a striped sweater for my son in the round (my first stripes!) I have the technique down and learned about joyless stripes, but am having some trouble w a certain aspect of the pattern. It’s knit in the round w purl stitches, but for those who prefer the knit stitch (myself included) it’s suggested to work in St and turn inside out in the end.

My problem comes in when working in a new color for the first stripe. I may be losing my mind but can’t seem to figure out how to keep the tails (and ugly little line form swapping colors) on the outside of my work since I will inevitably be turning it inside out for the finished project.

Am I missing something or is this not possible?

There is no way to correct that. It’s just the way it works when you purl. What pattern are you knitting? Do you have a link?

You can see from the pictures here that the back of the project gets the dotted line look.