That is a pretty cool toy. Does it actually run on steam power? I think it would be best to keep it as much original (as in present banged up condition) as possible, and if you add the missing pieces, they should be "antiqued" to match. It looks like the power to the rear wheels is applied by means of axle shafts using just friction drive to the rims. I wonder if that is how the actual full-size version works, or would it use some sort of gear drive? Not that I would change it, but just curious.
Ah, watching the video shows that they do indeed run on real live steam power (although not always reliably). Not sure it was a good idea to run them on a wooden floor?

And the wheel drive seems to be a small rubber wheel on the shaft. Still wonder what their full size versions use(d).