I think it might felt better, stay smooth & flat, if you re-do the top few rows in garter stitch.
when you don't know for sure the yarn content, to tell if yarn will felt you can do a 'spit join' - spit or wet/damp via other means 2-3 inches of 2 ends. lay them overlaping each other in the palm of your hands and rub your hands back and forth fast and see if they have joined.
Your handle idea sounds like a good one, though 10 strands might be too many for size 13 needles. You do want it knit loosely for felting. Your bag is knit loosly, isn't it?