There are a lot of factors here...I think nearly every member of UU would spend the money to have it fixed, and many of us would be willing to send it to Kamaka for repairs.
I don't own a Kamaka--but I probably will someday. I'm not sure if you are aware of this, but Kamaka celebrated 100 years last year with a special model--and nearly all of those should be out and for sale (I think Mim posted some today). I'll probably wait a few years (there is a Mainland, Opio, and KoAloha with my name on them first) and try to buy a centennial model at a slight discount (used) in the future.
Keep in mind that a new Kamaka tenor is $1400, and a new Kamaka baritone is $1600. And I'll be bold enough to say that a repaired "vintage" ukulele (we're talking 60s, right?) in good repair should retain a good amount of the value of a new one, and theoretically should have appreciated in value.
A good rule of thumb with ukuleles is to not buy as an investment (which is not the same as collecting), and for "players" to buy used, as the second hand generally takes 30%-40% the price of new off of an instrument.
Incidentally, Jake Shimabukuro, the ukulele virtuoso, plays Kamaka, and on his Nashville Sessions tour repaired 100 Kamaka Ukuleles in his travels.
If the repair is $350 plus shipping for the repair of an instrument potentially worth over $1000, and priceless as a family heirloom--get it repaired.
If you are looking to simply have someone else deal with it, name a price and there are members of UU who will step up--AND they will also let you know if your price is too high.
I'd personally repair it, keep it in a good case, keep it humidified in dry weather, play it a lot, and pass it down to my kids when I depart this earth.