I guess this doesn't help your search, but for all 5 of the transfers I've done I've just dropped the paperwork off in a manilla envelope with my cell phone number on the envelope at the CLEO's office. Usually within a few hours I get a call saying my forms are signed. This is with Sheriff Whetsel in Oklahoma county.
I'm guessing you're going to need a signature from a Tulsa CLEO, which I've heard is the one area in Oklahoma where you may have problems getting a signature or so I've heard. Your SOT should be able to tell you for sure. My guess is a cover letter isn't going to have much effect on whether the CLEO will sign or not, but if you're going to do it, then make it brief, simple and put some means of contact on it. Whatever you do in the letter, don't ramble on and on about why you need the NFA item or why it's justified etc...