Having to remove the axle shaft is simply a scare tactic. That is no harder than removing the rim and wheel off the axle. You have to jcak the unit up to remove them anyway. Should be something like 8 bolts in the center of the wheel hub to undo then pull the axle out. This is a picture of an older Dodge but the Chevy would be something simular:
Usually you do not leave the rim/wheel on when you remove the axle. You have to remove the axle to access/remove the adjusting nut so you can pull the drum off.
This is an older Dodge but Chevy would be simular.
Bottom line even with a labor charge of $125/hour it is not a $1100 job.