If I am reading your response right, you are doing the TransAm in stages? A folding bike will save you hassles at the airport and other methods of transport, so if that is a big factor for you since you'll be doing multiple trips, there is merit to considering one.
Something like a Bike Friday can be configured to ride just like a regular touring bike, however, it is not without a few compromises. Smaller wheels do mean more tire wear, so expect to change them more often. To get the high gears that some cyclists want, you'd have to go with a Capreo hub, parts for which a regular bike shop would not normally stock if it breaks during an epic tour. Also, if you do not have the right rack/pannier combination, there is more tendency of your heels hitting loaded saddlebags.
With regards to packing, I find it takes about the same amount of time and care to prepare my regular or folding bike for flights. You complained about a bent derailer — I never leave mine bolted to the frame, it takes a few seconds to undo it and tape/zip-tie it to the frame. Leaving such a vulnerable part on is asking for trouble. Despite just wrapping the frame in cheap pipe insulation and bagging it in clear plastic, I have not suffered any damage to my full-sized steel bike in over a dozen flights. The advantage of the Bike Friday is that it can fit in a suitcase, but if you're not doing a loop, you'll still have to figure out how you'll get the hard case to your endpoint. There's towing it, but that comes with its own set of compromises on shoulderless roads and busy urban areas.
Folding/break-apart bikes excel in situations when you are not riding the bike (like taking a plane, train, bus or taxi) and if those factors surrounding those situations are critical in your trip, take a folding bike, if not just pack your regular bike more carefully. If it is just flying that concerns you, most large planes are no longer loaded on the tarmac — containers shaped to the fuselage are loaded in the terminal which has reduced the amount of manhandling. In my experiences, a bagged bike is usually laid on the top of the container since it is odd shaped, while bikes in concealed boxes (or in a suitcase) risk being crushed in a pile.