Martha,
Aside from the breathing issue in the use of plastic is the purported factor
of free radicals released from the plastic if it is PVC.
I wish i could keep blessed chickens in my (leased )situation to do what you
describe...further processing the compost for you in a value-added way! It
aint lost.
I know, it can seem a bit untidy around the edges, and requires shovelling
up those thin edges before weed seeds really start up. Usually the heat from
that integrated chicken shit will kill the seeds.
And can't you also upend the pallets and continue your piles right and left?
....not knowing your entire situation...
...manfred...