Problem is, you don't just get called in for an interview and become a driver. Although it's possible on a 1 out of 6 basis (for every 5 in house advances into driving from PT, they may hire off the street). In my center, 1 person went driving over the course of 5 years. Took me 5.5 years of slaving away PT. It could take a center 10-15 years to to get to the point of hiring a guy off the street.
Sorry to burst you bubble but the reality is tough to swallow. You could look into it (depends on area), but I bet you'll be staying with your current job.
It's almost easier becoming a member of the US House of Representatives.