Hi CC,
As you know with my Petunia many times even if you do a digital exam and take them to a vet and do an xray it likely wouldn’t show a soft egg ‘stuck’ up high.
Also it’s pretty hard to say if the heat is stressing her or not.
As others have suggested I would give her calcium, for a few nights, I would also bring her inside a cool place overnight in a dark quiet crate. It could be that she is just heat stressed. I really wish we could talk chicken, don’t you?
How did she tolerate the bath? If she was good with that how about some cool water to stand it to cool her feet? There are all sorts of ways to cool them down - I think your brother made an evaporative cooler - maybe try that to keep her cool.
Another thing I give my egg bound girls is some aspirin - they are likley feeling pretty cruddy and the aspirin will help with pain and any associated inflammatory process. The dose is 1/2 tablet of low dose (81mg) aspirin.
If you remember, it took Petunia a couple days to finally pass her egg, she then passed a regular shelled egg right after. My Vet put her on Sulphatrim due to the fact she was bunged up. I would not try any antibiotics for your lovely lady, but pain management would be likely a welcome thing.
Another pain med you can give is Tylenol (infant liquid Tylenol 80mg/ml), the dose for a 2kg chook would be .25ml.
Gosh I hope she is doing better. Poor wee lass, it’s always sad to see our wee friends not feeling well isn’t it?
Keep us apprised please
Lots of love, CC!
so can’t even break the egg and try to extract. This happened with my Petunia. My Vet was hesitant to grope around too far, it either do exploratory surgery or wait and see. 
