This is some years out of date but might be helpful.

We flew to Boston with our Pino in two parts with Virgin in 2015 and it was very easy.  The Pino halves were wrapped in bubblewrap and put into the two 90 x 120cm canvas housses we already owned for taking the tandem on TGVs.  We also had a wheelchair, suitcase, sports bag and rucsac - see picture taken at Boston Airport.  We rented a modest (by USA standards) estate car to transport us to our start point, and for storing the wrapping while we were out on the road cycling.  When I did our pre-flight research, I found Virgin were very cycle-friendly and all the above items were included in our baggage allowance.  BA were sufficiently less promising that I didn't pursue that option.

Since that time we have added a small pedelec attachment, so flying is no longer a possibility.  Hopefully there will one day be a standard design of battery mount so that one can easily rent batteries at the destination, but at present there seems to be no standardisation in prospect.

Circe Helios (with couplings) fits in a standard (airline-wise) size suitecase (be prepared to pay for extra weight, it comes up to almost the limit, 29kg in our case).

I presume any sufficiently sturdy case will do; we actually use a special case made by Co-Motion (cause we have it already) https://co-motion.com/collections/store/products/co-pilot-bicycle-travel
but it's certainly nothing special about it - except that this case also can take a (single) Co-Motion race bike, with normal size wheels, which are the main size constraint. 

We did this trip in 2015.  We flew Virgin (who do take tandems) who now go to Atlanta and did the trip to Memphis in a people carrier as we had a full sized non splitting tandem.  Despite what any airline states you are basically at the mercy of the check in staff and baggage handlers.  We had a bit of wait on the return journey waiting for our tandem to be accepted by the local team at the airport.  We now have a tandem that splits into two cases and that is lot less stress.  We did valet parking at the UK airport to avoid having to take the tandem on car park shuttle buses.  At the US airport I got the hire car whilst my stoker waited with the tandem as it was a shuttle bus the hire care section.  I then picked her up at arrivals.

The Santana holiday was good but the rides were a little disorganised and required early morning attendance at the briefing sessions to find out where we were riding that day.  Hopefully they have improved over the last 10 years.

hope you have a great time

Andrew and Viv

Giles, Jane

Jen and I did this same trip in ?2015 taking our Thorn Raven with S/S couplings. Virgin Atlantic to Washington, hired a Jeep to drive to Memphis, hired a Jeep again for trip New Orleans to Atlanta, Delta Airlines home. No problems going or coming. Fantastic holiday, you will love it. Away at present, back 4 March and can help you more then. 

Regards

Jenny and Peter Weeks

Pack your bike expecting TSA to open up the cases and rummage through them while they are being transferred from your transatlantic flight your connecting domestic flight to Memphis. On the advice of our Denver tandem-shop owner before our first flight with our decoupled Co-Motion packed into its 2 cases, we cut 2 spent tubes into 3 lengths each, then used them to lash the frame pieces and wheels to each other, thereby preventing the inspectors from moving any of the carefully-placed parts out of position without knowledge of how to get them back into place without doing damage. The ties made the pieces a single blobluar unit -- still open to inspection but all pieces held in their proper place.

The Mississipi River tour looks like a fabulous trip; the Natchez Trace is a bucket-list ride for its beauty. 

Jeff and Kathy, Colorado (headwaters of the Arkansas and Platte rivers, which feed the Mississippi!)