I polish a good bit of stainless in my sculpture work.
I don't think your plan for the sanding process will do what you want. To achieve a tinted transparent finish such as Koons does you have to get the stainless polished to a mirror finish before applying the transparent coat. 240 grit sanding scratches are too large to remove with a buffing compound on a cotton wheel. Also to begin with 80 grit, unless the piece is scratched pretty badly, is usually excessive and adds to the work.
I generally begin with 150 (or 220) then 220, then 400, then 600, then usually 800. You must remove the sanding scratches left by the previous grit sandpaper before moving on to a finer grit or you will never get them out.
Then a fast cutting aluminum oxide buffing compound made for stainless will take over from there, on a hard sewn cotton wheel. Hard sewn
is the operative term here.
Stainless is hard—it eats sandpaper. And hand sanding is almost useless except on tiny pieces. I mostly use a 3 inch air powered disk sander (0 — 2500 RPM) with soft pads and Velcro disks that I cut out of 25 foot rolls; otherwise the cost can get quite high.