Revisiting this thread much later to post a couple of photos of my rinko-packed bike, which I successfully took on Amtrak from New York to Savannah, and later from Albany to Buffalo. In the close-in photo, you can see the (fairly crude) "Rinko Folder" stickers I put on the downtube.
My packing method is actually a slightly bastardized version of rinko. The bike has a 62cm frame and an exceptionally long head tube, and so packing the wheel with the fork attached (the standard rinko approach) creates a package that exceeds Amtrak's maximum folding-bike dimension by a frustrating inch or two. Rather that risk having someone get out a tape and make an issue of it, I pack the fork separately in the cardboard box I bring as luggage. No problems. I flew home from Memphis with the bagged bike as checked luggage. Delta charged me a not-at-all-outrageous $75. The bike arrived in Burlington, Vermont with me in undamaged condition.