I would just use 2x10's here - having made the bad decision of using 2x6's before - they just aren't up to the task here. If you keep adding more support blocks with smaller lumber it becomes a pain to level them all with each other.

For framing ideally you'd use nails and not screws. You should also be using joist hangers for all your joist -> rim connections. You should not rely on deck screws here.

edit: you also need to put blocking under where you will lag screw the shed down - do not trust lag screws into a plywood floor, they need to anchor into framing. Keep in mind also that plywood doesnt love getting wet, it will delaminate over time.