$1000 is from a shop that already has more work than they need.
$400 is about right. $100 parts + 2 hours of labor. Yes, a shop should be able to do it in less that that but they will almost always charge the book hours unless you're a regular customer.
I've done it myself and it is a royal PITA due to limited access but it can be done in a couple of hours. Just know ahead of time that you're going to cuss a lot so pick a day when the kids aren't around.