I found something while reading tonight that I think will be of interest to you.
I have a text that recommends in cases of egg bound hens that mineral oil be applied into the cloaca, and using one finger gently you insert into the cloaca, the other hand against the abdomen, to try to gently ease the egg out.
It also says that if the egg is absolutely too large, that you can direct the egg towards the back of the vent, pierce the eggshell and crush gently to make it smaller, and then remove it AND ALL portions of the shell. NOT that I would recommend this to anyone (I like the former version). But I had remembered hearing of this but just knew something was missing that made it very bad advice as presented.
But what I NOW remember having also heard is the very very very important next step..
As the book puts it, you then use water and a very mild (internally safe) antiseptic to flush absolutely all of the egg contents and bits of shell from the vent, and they recommend that it is cool to help decrease the inflammation as well as remove all the contaminants.
I'm thinking a saline solution of the type that you'd use for wounds (the weak solution), or possibly Nolvasan mixed with much water. It may be too late for this, but maybe not. That's what I would do if you hadn't.
I can reference the book, but will do tomorrow. I just had to type this in case you were up tonight. (Boyfriend is like "You're going to type that now??" lol)