"The correct repair is apparrently to dry out the fiberglass, remove the saturated balsa, and fill the resulting void with fiberglass resin. "
The catch there would be trying to remove the balsa and get clean surfaces, without removing the lead. Removing the lead by lifting, as a piece, may not be possible. cutting it up, a nasty job. Opening the keel shell and dropping it, nasty and expensive.
Which leaves you to consider a kludge job and gamble on how well it might work. Draining it out, covering it and adding a hot air dryer to push out more moisture, adding alcohol and letting that pull the water out...you might try something like that and then pouring in epoxy
penetrant or thinned epoxy
to solidify whatever is in there, might be a good enough compromise.
I hate to say "might" and "kludge" with a keel but considering the options, I don't see any other really good ones. Given the large amounts of surface area involved, I think "dry it out and glue it down" might be fairly reliable although I wouldn't want to roll the boat over to confirm it.