I use mostly pillow ticking as patch material cut at the muzzle. The ticking is measured with a dial micrometer by using the thumb wheel at the end. When the jaws are snug that is the measurement that I use. I just measured some ticking using a dial micrometer and caliper. I got the same reading but had to use firm thumb pressure on the caliper to do so. The caliper squeezes on a broader area and the mic on a smaller one. From my test use good firm thumb pressure on the wheel of your caliper and you will have a good measurement.
I too buy ticking in bulk from fabric stores. Look for ticking that has minimal (or best no) sizing on the back. You can tell sized fabric because it is shiny and kind of slick on the back. Wash the ticking prior to use then cut in 2” strips. I roll up the strips and bind with rubber bands.
Your plan for lubrication is fine, although you may have to scrape off excess lube. Because I’m storing the ticking for future use I’m careful not to pick up grit. This is much more of a problem if I prelube the material. Normally when shooting at the range I lube the ticking with some homemade soluble oil. Any commercial lubricant should work well as will spit.
Cutting patches at the muzzle ensures that the ball will be centered within the patch. From doing it both ways I don’t see a significant difference but this does remove a variable.
I know that I don’t need to say this but.....Sharp knives are used to cut patches at the muzzle (a straight razor is a great patch knife), use caution when cutting patches and cut away from your body.
Take care and have fun,