I always used a wheelbarrow because it seemed easiest and fastest. Then a guy came in to clean my yard and he had to haul around a lot of bulky but light stuff.
He just used a 30+ gallon plastic trash can with beefy handles. That was much lighter than a wheelbarrow, and he could drag it around faster than I could maneuver a wide wheelbarrow around obstacles. 30 gallons is 4 cubic feet, and he could stuff that thing tighter than I can stuff a wheelbarrow, and nothing spilled over.
You might find a plastic garbage can useful in narrow spots! I would reinforce the bottom rim with several layers of duct tape or one layer of Gorilla Tape, so that scrapes don't wear away the plastic.
But a wheelbarrow is still better for heavy stuff.