I can tell you that management will most likely take a percentage of all income (gigs, merch, cd sales, etc.) regardless of if they got that work for you or not, as well as a payment on a regular interval (monthly, quarterly). I am managed by Intromental Management
. Their US operation is in NC, so they're not too far from you - but I don't know if they're accepting new submissions or not.
All management companies are selective in who they work with. It's a business for them, and if they don't think the band will generate income they won't take them on. Be prepared to be turned down by multiple companies before you find one that wants to work with you.
I seriously doubt that you'll find a management company that will book a radio tour on percentage, given that you're not getting paid for those appearances. You should also think about if you want a manager or a booking agent. A manager will handle every aspect of the band - from dealings with labels, to concert bookings, to career advice. Most will not provide accounting or legal representation, though they will have companies they recommend for those services. A booking agent will find you gigs, and that's it.
If you're not playing out at all, I'd be hard pressed to suggest that you go the management route unless you have some deep pockets. You're looking at spending a lot of your own money on this - probably over $100 per month, plus a percentage of any income the band makes.