Try begging and pleading, but I suspect they'll just stick to their guns of charging the early upgrade fee. But who knows, maybe you'll get lucky.
I expect they'll offer getting a phone on Next, but that's not a wise choice unless you were planning to get off of a contract subsidy plan anyway. (though it might be a good impetus to do that analysis to see if Mobile Share is a better choice vs. your current plan -- depends on several factors specific to your usage and future plans so you'll need to consider your specifics vs. any generalizations suggesting which path is better)
You mention that repairing her current phone would induce her to keep it. Why is that? Wouldn't she have already traded in or sold her old phone? With a busted phone that value is lost, doing a repair merely recoups that value -- and whatever the difference is beyond repair cost and what you get on trade-in or resale is the price of having a phone for the month. Still probably far less than the early upgrade fee.
Another thought - pick up a basic go-phone and put it on the line until she can upgrade.
EDIT: have you considered trying out T-mobile?