What is the humidity in your house?, your heat source? Sometimes, it becomes necessary to run a humidifier in the incubator room. I've never had to do so, even with wood heat, but have heard of folks who have needed to do so.
Have you done a salt calibration on your hygrometer? Perhaps spray down the walls of your bator at first pip?
Are you sure that shrink wrapping is your issue? I get good hatches running at 30% until lock down. (30% is my goal, but during that time, a reading may be as low as 11% or as high as 40%.) For hatch, I bump up to 65%. When the babies start hatching, they will add to the humidity!
Monitoring air cell size is my guide. If air cells are too small or too big, according to the development charts, I then adjust the humidity accordingly. At times, I've had to run completely dry from day 14 through first pip to get air cells where I want them. Particularly if the outside weather is humid. If air cells are too small, the chicks drown when they pip. An other factor associated with air cells being too small is: the chicks grow too large, then can't easily hatch.
I use sponges as humidity source throughout my entire incubation period. Stand them up in a cup of water so they wick. Adjust size of sponge or number of sponges according to need. I cut them into 1 - 2" strips to make it easy to adjust. I've even resorted to screwing an extra sponge to the side of the bator b/c there was no floor space to accommodate the extra sponge needed during hatch.
You mentioned water trays and sponges. Are the sponges laying flat in the trays? If so, that may be your problem. If the water level is close to the top of the sponge surface, you're really not gaining any surface area by adding the sponge.
And, finally: are you opening that bator between first pip and last hatch? I will open the bator if needed, but only if my humidity is staying up, and I know a drop will only last a minute or two. I keep humidity up in bator with a syringe and aquarium tubing so I don't need to open it to add water.
Are they hatching between day 20 and day 22? Does their development (when candling) match the embryonic development charts? Is it possible you have some genetic issues? What breeds?
Just a few thoughts.
Agreed, having a broody takes the guess work out of the hatch. I've enjoyed my broody hatches. But... it's nice to know that I could return to bator if necessary. Nothing as sweet as holding that warm egg in my hand and seeing the little chicklet dancing in there!!!