@Cody I am currently in a similar situation with The Lucky Needle. I would love to be able to focus %100 on the business but its not enough to to make ends meet yet. I understand the frustration and anxiousness.
My suggestion to you would be to raise your prices. Unless your already charging comparable prices to the top shops in town. Your in a good position now to raise your prices and build a better customer base because you have the security of your full time job to support a loss in business. Also start booking jobs out farther. There are lots of shops that have a year plus of work booked out. You can do the same thing. Your in a good position to start building a strong business now while your expenses are low and have consistent income. Set your self up for success before you make the leap. Get clear on how much money you need to make monthly in your business before you leave you job. Save up a nice safety fund for when things don't go as planed.
As far as bringing more work in other than word of mouth. Most important thing I think is build a website. You need to have a website showing off your work that people go look at before they call. Think about it. When was the last time you used a business with out checking out their website first? I know I wont even consider calling a business without a website.
Add your business to all the online local listing sites like yellow pages, yelp, etc Ive gotten a lot of customers from this.
I also suggest expanding outside of just auto upholstery. I always focus on Auto , Marine and Commercial furniture. Ive always been able to make good money on these types of jobs. And it helps limit your exposure to just cars. Plus the skills are the same so why not.
This forum topic on pricing might help you as well.
viewtopic.php?f=7&t=14
I hope this helps.