I cant pull a quote regarding bed ticking haversacks out of my records, but I do remember a refrence to bed ticking shot pouches for the Govt troops during the NC war of Regulation. IIRC they had a brass button as well.
But yes, I would say make it out of the same material, aprox 2 inch wide strip, perhaps 2.5, whip stich it closed inside out, Turn it right side out and then run two lines of back stitching down the length aprox a quarter inch in from the edges.
If you attach the strap by sewing thru the flap and back, you eliminate the need for 3 buttons, or any buttons at all.
I google search on British Military Haversacks should return images of a surviving haversack used here in North America and a how to on reconstructing one.