Yes- There will always be one in the southeast. Been there, done that. I forewarn you, this is a long post.
By mulching I'm assuming you mean with something like this:
If so, you really need a big rubber track loader with high flow hydraulics. Cat probably has the best machine on the market right now with the 299 XHP with a forestry package, a machine that will set you back a little over a hundred grand. You don't need that big of a machine, but you do need high flow auxiliary hydraulics.
I disagree with northman on taking out a loan on this piece of gear. Skid steers & CTLs don't generally last very long in terms of hours, so I would buy new if possible. 3,000 is the mark where they start to need some serious TLC, but the nice thing about a skid steer is that most components are small and you don't need a huge shop or a crane to rebuild 90% of the machine. I love my 287, but it's my oldest skiddy and it had 3,561.87 when I parked it Friday. My Case 435 S3 has 5,000 right now, and it's about at the end of its' life.
The other thing about putting a mulcher head on a skid steer type loader is that even if the machine isn't running the mulcher you can keep it busy. The other other thing about putting a mulcher head on a skiddy is that they are really hard on the machine. So the ~3,000 hours is even more important there. But if you charge appropriately it won't matter. And be damn sure to clean your radiators, air filters, etc and check for damage to your hydraulic lines and stuff at least once daily. A lot of these machines burn up because they get pushed really hard and get hot.
If you can't buy new, I'd look at a low hours (less than 2000 is what I'd go for) C or D series Cat machine with high flow and at least 80 horsepower and high flow (287,289,297,299) or a Bobcat T300 or T320 with high flow. Not that other companies don't make good loaders, it just seems like Cat and Bobcat seem to run mulchers better. I like and use FAE mulcher heads. Fecon is another great option.
Good luck with your endeavour!