Don't have this problem often (yet), but was so disturbed at the odors and obvious health hazards associated with disposing of poopy diapers. Really, these are toxic biohazards, as are baby diapers, but doubt the hazmat teams will come out and collect our soiled diapers and paper towels.
This is the solution I've come up with so far, however just on a diaper at a time solution. Here it is.
Get two layers of plastic bags into a waste bucket so you'll have two bags ready to help seal odors. Buy a lot of that super absorbent cat litter, perhaps with odor control. Put a few cups into the bottom of the bag. After removing and flushing large pieces, put the diaper into the bucket with poop showing (don't fold diaper over) and pour cat litter over all poop to absorb the moisture and odors. You can continue putting in wiping clothes, and pouring over more litter as needed. Seal up the inner bag. Pour some baking soda over this inner plastic bag to help cut odors, then seal up the outer bag.