Yes this is very helpful. I do feel like I should add that I have noticed another Pullet with dirty butt feathers. Does this change anything? Just in case it's helpful at all, my 5 big girls consists of 2 SLWyandotte's, 2 Barred Rocks, and 1 Buff Orpington. The other Wyandotte, "Fashion", is the other pullet with dirty butt feathers. The 2 Barred Rocks are the only 2 out of this flock to NOT experience dirty BUTTS (not sure if the fluffy feathers in the other breeds are notorious for being messy or not). Right after Thanksgiving, 2 of my 3 boys had messy bottoms and I only mention this because the boys sleep in the girls run at night, but they're ALWAYS separated by something, whether it's the run Door or fencing when they free range. I clipped the boys feathers and figured the kitchen scraps my neighbors shared with them was the culprit. Back to the big girls, all 5 seems to be moving around like normal and dust bathing. We've had a very mild winter up until last night, today and throughout the next couple of days. We're experiencing lows of mid 20's and highs of upper 30's, which isn't that bad to many, but it did seem sudden for my birds.You really do have a lot to sort through. So, what I would do is nothing for the time being except watch closely for any "off" behavior. Getting a poop sample tested is called for if you suspect parasites, coccidiosis or a bacterial infection. It may be premature to suspect these after finding the smashed eggs.
A hen can have an occasional thin shell egg and it won't be a problem unless it becomes a chronic thing. Then you need to snoop in the nest boxes to try to figure out who is having this issue. It's the only way to resolve it without treating all the hens, which is not practical.
If you have a suspicion who the hen is, you can verify it by placing her in a crate inside for a couple of days to see what sort of egg she lays. Then you will know it's the right hen to treat if you get a collapsed egg. The treatment is one calcium tablet per day until the eggs become normal.
Laying soft eggs and thin shell eggs as a chronic issue is risky for the hen as eventually one of these eggs can collapse inside and then you risk infection and also need to help her expel the remnants.
Is this any help? Ask more questions, if not.