Don't go the corporation route unless you have to. When your corporation buys an NFA item, it pays the $200 transfer tax. If your corporation closes, you have to transfer the NFA item to yourself or sell it to someone else. That means you get to pay another $200 tax if you keep it and still have to get the CLEO to sign a Form 4.
Just call the sheriff's office and ask them. The county sheriff office where I live has a secretary to handle NFA transfers. You take the forms to her, she runs your name through NCIC, you pay her a $25 handling fee and leave. She keeps the forms, gets the sheriff to sign them and mails them to you. It never takes more than 1 or 2 days to get the forms back.