Just adding my two cents. Having built an arena and “dry lot”
Arena has 2" base rock (that sat for a winter/spring), fabric, 4-5" of the fine screenings, then a couple inches of sand. Zero issues with drainage or fabric coming up. Love my arena. DH works in construction and did this with a skidsteer and laser level he borrowed from work. Other than the original dirt work which we hired out.
Dry lot had 2" base rock, 1" rock, and we’ve slowly been adding screenings. It naturally had a slope thankfully so didn’t have to do dirt work. Absolutely hard and never has mud or issues where the rock is (we only have done about half of the lot at this time because money is a factor). This was all done with a tractor and bucket.
We have sandy loam and live in the Midwest.
All to say, I don’t think you need 8". Feels like overkill. To save money, I’d do a layer of base rock and maybe 3-4" of the screenings. And I would feel really confident about that. YMMV.