Not sure what you mean by "Hitch Haul", but if you are referring to a bumper Lunt hitch, don't do it. Now the modify part, if you are going to tie the Hutch Haul into the frame of the trailer, then that is probably ok for the waste tote since it if lightweight.
For firewood, you will have to be very careful (even with the waste tote, but since the wood weighs a lot more!) not to haul to much as it will decrease your tw possibly to the point you have sway from not enough tw. If you have the room, buy a larger Rubbermaid tub (or 2) to store the wood in. Depending on your vehicle or trailer floor plan, the tub will keep the inside a lot cleaner. Just wipe down before placing inside each time.