Whether the "bedding" needs to be absorbent depends on what it is trying to do.
For areas where chickens actually poop, I agree the bedding does need to be absorbent.
But inside a nestbox, it does not really need to be absorbent (example: plastic nestbox pads).
And if the hen really does all her pooping outside, then the bedding is more for comfortable walking on the floor than for any other purpose. Again, not too much need for absorbancy in that situation.
That definitely sounds like it is worth trying. Fluffing the shavings each day could help with them drying out.
Depending on the humdity level, you might just be stuck replacing the bedding frequently as the only way to keep it dry.
Or maybe use something like old towels, where you can put in a dry one and hang the damp one up to dry. Hanging in the sun might get it more dry than sitting in the coop. For other kinds of bedding, it might also be an option to cycle it in and out of the coop to dry, rather than using completely new bedding if it is only wet not dirty. At least, that might work if you have some periods of dry weather to work with. If the weather never gets dry, obviously that won't work either.