What I've found out about using tarps under the load is you aren't limited as much as you would think to the size of the load.
Just use more tarps and layer them in the load. Just don't load any single tarp more than you or you and your helper can pull/roll off.
Another nice thing about the tarps is they don't have to be on the truck when you load them. I can dump the grass on a tarp in the back yard and when done drag it to the truck, grab all four corners, and throw it on the truck. Often this is how I will start the next layer.
One area that this doesn't work well is with tree limbs and brush. But thats another situation.
I have done this with mulch and it worked pretty well.
I agree with those that say a dump bed is best, but This is alot cheaper and almost as fast for me.