However the support person is now insisting that in order to change my email, I must first change my last name to remove the apostrophe there as well.
Ask them whether that will change your legal last name on your paystubs that go to your version of the IRS (taxes). If that is the case (and it will), tell them you will not be part in falsifying any legal records.
That they transfer last names exactly into email addresses means those IT people are clueless morons. It does not work for so many last names, not only your's. And it hasn't, for decades. It's not that your name is somehow new to this world. IT people had to deal with names that do not make up valid computer usage all their life. The US invented computers and used a very limited set of characters, that wouldn't even work for all languages spoken inside the US. And certainly not outside. We have dealt with it. Having a valid email addess to any given name is not rocket science by any means. It might be a good practice test for IT people's first year exams. But it's certainly not a hard business problem for anyone having finished their education.
Obviously, you cannot tell a stupid idiot they are a stupid idiot. So just tell them you won't be part in changing your last name on legal documents and let them figure out the rest of it.