You can download the radio schematic
here.
I've been slowly restoring a Radiola 82 which has a very similar power supply / audio amp chassis. All the capacitors are tar filled metal cans and are quite likely still good. Even though my radio was operational, I did choose to restuff them. It's a messy job, but I figure it'll be good for another 80 years now
You can read about it
here.
I've never worked on an RE-57, but I do have a chassis for an RE-73. The mechanical tuning mechanism is a real work of art!
I don't have a cabinet for it and plan on parting it out. So if you end up needing any replacement parts, let me know.
Good luck,
Bob