One way of solving the problem is to do something similar to a Bailey comb change, but with two different sized boxes. Put the a box of the desired type with foundation (Langstroth, in this case) on top of the established colony and let the bees move up over the course of 3 weeks.
You need an adaptor to go between the two boxes. If you're going National-> Langstroth, a Langstroth-sized sheet of 9mm plywood with a roughly circular 16-inch hole cut in the middle would be ideal (needs to be fairly thick in order to create a bee space given that the Langstroth box on top has no bottom bee space and assuming that the National underneath has bottom bee space as opposed to top.
A more violent variation on the theme would be to do a shook swarm into the new box size and let them establish for a few weeks.