How to alternate two yarns (2 rows each color) with a slipped stitch edge

I am trying to alternate to similar color hand dyed yarns to prevent stripping and my pattern states to slip the first stitch in every row. I can’t seem to keep the nice edge now that I have started using the two yarns and need to know what the trick is to keep the nice chain looking edge. This edge will be highly visible in the finished garment.

The problem is the carried yarn which shows along one edge?
Since the yarns are similar in color, you could switch yarns say, two stitches in from the edge. For that matter, you could switch yarns anywhere along the row except at the edges and preserve nice slipped stitch edges. The carried yarn should then be hidden.

If you’re making a scarf this won’t work so well however.