One I welded together out of scrap. I don't think your plate is going to hold up. Why stainless, you can find some scrap steel plate for free just about any iron railing, welding shop. Some of those guys are shooters and will weld you up something for minimal costs. I'd shoot for 1/4" on that back plate. This one has about 100,000 rounds splattered on it. No bulging but it will not hold up to larger caliber pistol rounds and rifle rounds will go right through it.
Your lead is going to splatter off the the spinners so careful of what is up, below and to the side. You might make the backstop so that the spinner could sit just inside of it. The lead also splatters off of metal backings, notice in mine all of the lead plastered to the sides and bottom of the contraption. I've actually had lead splatter back out of these with enough force to draw blood at 50' if hit in the neck or face. So keep the eye protection on. I now put a board on the front to catch any splattered lead but that only works for just so long before it is shot to doll rags.
Make it large enough so that you don't miss should you try a little faster shooting action. My 2 cents.