Hey Smokey,
You could add/sew a circle of leather to the front and back of the woven strap, and sew your hangers to that. Lots of options. You could sew a back-to-back pair of buttons on the strap too as something to which you could affix a hanger.
Jim Webb told me that the old guys did not have their accoutrements dangling from their straps. Too much chance of noise, movement or loss from catching on something. They were tucked under the side of the flap and into the bag unless the shooter was loading.
I hope this helps. Marc