As mentioned, use a non-cutting needle, or dull the cutting edges on the included needle. The strap is a machine, like a rope. Cutting strands here and there reduces symetrical tension distribution and greatly decreases strap life and rating.
Pic attached shows one set I've made from old fall poly strapping salvaged from a quarantined SRL from work. I overkilled the stitching using 80# waxed nylon @ 70 stitches per loop (just figured I'd match the rated load of the strap @ 5600#s).
I've been using awls for most of my life with leather and synthetic fabrics. As stated, "it ain't always purdy, but it's satisfying!"
Careful about trying to hold material in your "other hand" while stitching. Those needles pass real quick through fingers. The resulting bloodletting stains projects and minor discomforts reduce the efficiency of the rest of the project.
2nd pic is of my awl loaded with 40# nylon through a machine needle. I normally do not respool for this. Just thread as normal, loop around tension tack and feed off of regular thread spool.
I've used both the Speedy and Tandy styles mentioned. Both are useful. Thicker threads are easier to tighten in the material with the spool near the needle. My current one has the thread in the handle.