Perhaps 'The Insulator' on the Forum will stop by to add more info. FWIW, I have blown cellulose insulation. It, too like yours, is about 3-4" above the joists. This is because it's density-to-insulation ratio is such that it needs to be that high to be equal to, say, a comparable fiberglass insulation that fits EXACTLY between the joists. See what I mean? In 1 scenario, you need about 10" of insulation to equal R-30, and in another scenaril, you need only 6" to get R-30. (Or something like that ...)
Certainly, you can compress it but you'll lose some of your R-factor. (We have about 1/2 of our attic covered w/plywood but the house is pretty warm in winter and cool in summer. It's safe to handle with a mask, long sleeve shirt, long pants, and gloves. It's a very 'loose' material that you really don't want to breathe or get on your skin. BUt you can handle it. If you want to put plywood down and retain the FULL insulation value of R-30, you could substitute fiberglass batt insulation for the cellulose where you put your boards down. That's not much work (just watch your head on those roofing nails!) Or, just #$%$@ it and put the plywood down like I did. Remember, my house seems pretty tight based on my utility bills and so forth.
I'd pre-drill the plywood and joists, and only put screws down at the corners and a couple in the 'run' of the sheets. This way, in the future, should you want to run some cable or wiring or something up there, you don't need a hammer and a claw to remove the boards. Our attic, too, is for storage too. Oh, DON'T go piling things up real high. Keep your stuff out of the cavity/space between the roof rafters. If you don't have soffits and a ridge vent, consider these at some point.
My best to ya and hope this helps.
PS: In the meantime, I wouldn't store things like paintings or things that will 'rapidly age' due to the extreme heat and cold in an uninsulated attic. We keep toys and a crib and boots and some old kid-clothes up there. If any of those things get ruined either by the temp. or by mice/squirrels/whatever, it's no great loss.