@AnneInTheBurbs congrats on the new chicks! I love the heat pad tunnel!
Why did he think you wanted a truck? If you have a truck it is only natural that you will fill it with goodies on a regular basis.
I vote metal roofing...create a knee wall extension by making a frame out of 2x2s or 2x4s with 3 or 6 inch uprights. Basically it will look like a narrow ladder, lay it on its side on top of one of the existing walls and secure it with wood screws about every 8-12". Lay 2x4s on their side from tall side to short side, securing with screws down into the top plate of each wall. Overhang about 4-6" on each side, these are your 'trusses'. Make sure to have a truss flush with each end of the run since they are also where you staple your hardware cloth.
I think the metal roofing will weight slightly less than the plywood and won't need waterproofing. A flat wood roof will not hold up well, so even if you opt to use plywood for your roof you should still build the knee wall so one side is taller. A difference of 6-8" will provide plenty of slope for a 4ft wide run.
Tip... a standard 2x4 is actually 3.5" wide, for quick and easy spacers I would take a scrap piece of 2x4 and mark it every 3" and cut it. Then use it for the spacers by just laying them on their side, bingo...all are identical height and sandwiched between 2 2x4s it will give you a total height of 6.5" for the wall addition. Just angle your screws in when anchoring it to the base wall.