One last thing...if it were mine... (when reading the following, keep in mind that I am not a vintage collector type person...I play my ukes and value performance above all else).
That said, if it were mine and I liked the way it played I would probably convert it to a string-through-top by drilling small holes at the saddle end of the string slots, straight down through the top and the bridge plate underneath. You push the strings in from the top, fish them out the sound hole, tie a knot and then pull them up tight. This way you don't have to worry about whether the bridge is going to pop again with modern strings (modern strings tend to have a bit higher tension than old ones) or because the previous repair job was not well done.
I know,
some of the vintage fans are cringing, and if you do this don't ever take the uke on "Antiques Roadshow"
Just for the record, though. If I ever do happen to find a vintage uke I really like and buy it...I will probably be converting the bridge to a string-through-top even if it is pristine. So there, vintage fans
John