Tom, here are three that we know of that we feel comfortable suggesting.
4524 Dunning Road
Norfolk, VA 23518
Brunswick Landing Marina
Cobb's marina was used by a friend with a catamaran, and we saw their work. Good people, friendly, helpful. I assume their prices were reasonable because our friend looked for that.
Thunderbolt marina has a very good reputation and can handle massive boats, so your cat would not be a problem. Don't know about prices, don't think they're cheap, we've never stayed there.
Brunswick Landing marina is in a "hurricane hole". I'm fairly sure that your boat can be hauled and stored there. but you'll have to talk directly to them. Lots of Canadians leave their boat year after year. I don't think they're a bargain operation, you'd have to compare.
I used to have the name of a well-recommended marina in the Carolinas - South Carolina, I think, but I can't find it. I'll keep looking.
The issue is going to be the beam of your cat, so you need to talk with each yard about it.
If I hear of more, I'll post them.