I did one of these radio some time ago and I don’t think I had a lot of problems.
I do know that one one of these [maybe it was the Buckingham] I had to restring the tuning dial assembly with the thin
metal wire. It was a bit of a chore,but I believe that all the wire was there and it had just broke,
so I knew how it was supposed to go back together. Either way it is a bit of a challenge.
The models 10-57,,,10-58 and 10-59 are supposed to be the same radio.
If you have the RCC disk it is page 7, 1, and 12
As you say , some of the caps are on boards,and you can usually take out the screws that hold the boards in place,
and kind of bend the boards a bit to get at the caps. I cut the old caps off as close to the cap as I can. then make a J hook and hook the new cap to it.
Hook and solder the bottom first then do the top portion.
Here is a photo of my rogers 10-12 showing the caps on a board.
Dan in Calgary