Assuming you want the band permanently attached to the hat ...
How you attach the concho strap kind of depends on how it all comes together in the back. Some options are to use Chicago screws or hand sew.
Is it going to join between conchos, or under one of them?
You could butt the ends of the band and use an X stitch or a corset stitch. You could skive the ends to a taper and overlap them.
Maybe all the parts could join at center/back between conchos, everything could butt together and use about 3 rivets on each side of the joint to join it to the hat.
It you want it removable, I would skive the ends of everything to a taper, glue and sew them.
You could look at how bullet loops are made on gun belts for how those conchos might attach.