Strap construction and stitch alignment

[JZC]

I'm hoping someone has ideas on how to construct this strap so the stitches look clean on both sides.  The strap ends will go through the bag and wrap on both sides which will be visible from both sides.  My initial thought was to double up the strap ends (without the strap attached) and punch holes, hand stitch the middle section (where it goes through bag), attach strap ends through the bag, double stick tape (or glue) strap ends to strap, and then hand stitch with awl.  Am I on the right track or does someone else have an easier way or thought on a different process.  Thank you in advance for any advice.