So, when the opportunity to go to St. Louis presented itself, I told myself that I wasn't going to rent a car; no matter what. So, I didn't.
I packed Brahma in the B&W case and checked it on Southwest Airlines. Remember - 2 free checked bags up to 50 LBS on Southwest. The bags have to conform to airline checked baggage standards, which I believe are: Length+Width+Height <= 62 inches. I had no trouble with the weigh restriction or the size restriction. I kept nothing else in the B&W case, except Brahma. I even took the saddle out; although, my saddle is on an extended seat post, which makes it unnecessary to remove the saddle from the seat post. I took it out because it was easier to pack the suitcase without the saddle in there; too cramped otherwise. I might change my mind on this in the future though. For this trip, I stuck the saddle in my T-bag and checked the T-bag.
I want to take this moment to thank Fernando of The Dirty Brompton. Fernando's post showed me a very fool-proof way to let the TSA know how to open the case, without accidentally breaking it. The directions written on the B&W case, pictured below, are Fernando's original thoughts.
PS. I carried the Metallic Silver marker I used for writing the instructions on the B&W case with me to St. Louis. I needed to touch-up some of the letters, which had faded in transit. I think it is not a bad idea to do this.