I suggest using the stock transformer. If you really don't want to, send it to me, I would love to have a spare, they are very nice, and with the mount and shield would be very useful for other projects. And yours will have the dual primaries... Mine is single 120V
The KAB supply is a SMPS and so in a matter of speaking, pre-regulated. (The KAB is quite nice by all accounts.) I'm not sure if having a 317 based pre-regulator would be all that beneficial in the outboard supply. I would try a shunt regulator or a simple capacitance multiplier in the outboard, (or just more capacitance or RC stages) and then some kind of modern regulator (317 or something more fancy) in the TT chassis.
That said, your ideas seem quite sound, and are worth a go. :)
IF you can wait a bit (I'm out all next week for Captain recurrent training) ((I sit in the pointy end of jets for a living)) I am working on an easy LM317 based reg for inside the chassis. (The KAB DC-1200 is a LM317 design) After that I will try another configuration for the internal reg. (A "Tracking pre-regulator")
I will make a layout, plan and BOM for the simple configuration to be assembled on a small piece of stripboard. I actually knocked it together point-to-point, but a board would make things much easier.
Stay tuned!

