Dumb question but what’s the downside of having half the maybe 4-8” below ground level?Those earth anchors would be absolutely fine. They're not easy to install, and usually require specialized equipment, but the cost would likely be lower than concrete. I would use concrete because I can do it myself and I know it's going to be solid. You have no frost line, so you're looking at 2 foot concrete support piers. And I would not dig down, but elevate the building. Having a wooden building below ground level is just a recipe for rot and termites.
If Tuff Shed is a decent company they'll work with whatever anchoring system you decide to go with. They'll also object if something is inadequate. They don't want their shed to shift/move/rot/do anything bad. You should talk to them to see what their preferred method is. You might even be able to get a discount through them to get something.
If I raised the entire thing any ideas for how the ramp into doors would work? Extend the lower most perimeter to be a retaining wall a little past the ramp I think?