What a wonderful set! I would hold out and watch for a correct replacement transformer. The radio's not going anywhere and you can enjoy it as a unique period piece in the meantime.
If some day in the future you put it up for sale, the people willing to pay big bucks would care whether it has the right transformer or some other thing that's jerry-rigged to work.
Connecting the replacement transformer might seem confusing, but it's not rocket science. There are plenty of armchair quarterbacks in this forum and others who will help you get it right, when that day comes.
I do this rarely, but I'd also be tempted to "restuff" all of the capacitors when you reach that stage. This article has general info about recapping and links to other articles that describe restuffing electrolytics and paper caps:
http://antiqueradio.org/recap.htm . That's another decision you can defer for now, though. I wouldn't replace any caps until you have installed the replacement transformer.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html