First, let me say you can trust John, (tvguit).
Second, that's a neat guitar. I like the way you can see the outline of the original Bat Wing bridge.
I have a 1939 J55. The 1939 models were unique in that they had the stair step headstock and the mustache bridge. It was also the year the fewest were made, only 55. I say this to help you with a ballpark idea of value. Mine has been refinished at some time in its life, but otherwise is original. Some people say that kills half the price. Having said that, this one was appraised a while ago by Mandolin Bros at between $7K and $10k. I bought it from a private individual for more than 7, but a lot less than 10. It plays and sounds great. I just came home from three hours of jamming with it.
That guitar deserves to be saved. Obviously there is going to be $$ involved in getting back to playable condition with the correct bridge and that should be done by an expert. How much work it needs will affect the price you can get.
Thanks for bringing that out to the light of day. Good luck and let us know what you end up doing.
Rich