Some people on the other board have said that theaters are cracking down on audience members using COVID positivity as a reason for switching, and they want to see proof of a positive test. So I wouldn't start going down that route.
I am surprised Telecharge won't let you exchange. The box office for the week Jackman was out shows that a surprisingly large number of ticketholders did not ask for an exchange or refund. Even with Jackman out, the show still had an average ticket price of over $200. I might call them and try again, emphasizing that Foster, not Jackman, is the whole reason you are seeing the show. And as Guillaume says, if you go directly to the box office, that might work even better.