While searching for info on Katy trail in Dallas. I came across a 220+ mile rails-to-trails project in Missouri also called Katy Trail.  
     http://www.bikekatytrail.com
I want to ride this!  Since this is a railway it will be very level with gentle hills.  It would be possible to ship the bikes to St Louis and fly on Southwest Airlines.  Then pedal to Kansas City and fly SWA from KC back to Dallas.
 
For shipping we could rent a cube truck.  When I went on the Austin to Ft Worth ride last spring they had a cube truck.  First they put a layer of bikes leaning upright with large sheets of cardboard (from Bicycle's INC) buffered between the bikes.  Once the first layer was complete.  They began to stack the bicycles on top of the first layer.  They said when the ride had a 40+ people they would rent a Greyhound Bus and put the bikes below.  I think this would be a little snug for recumbents.
 
Terry
 

How about we just go ride the Mineral Wells Rail Trail, instead. It's 40 miles, out and back, and the Weatherford end of it is within a hour drive of my house. It's also a hard-pack trail, requiring wider tires.