The best solution I've found for these is to saturate the top with a solvent like naphtha or white gas, then apply heat to the top, for which I find a match tends to work well. Do this outdoors with good ventilation, and in just a few minutes the cracks will be entirely gone.

Seriously though, I second Chris on this one. Big can of worms, low value instrument, increase in resale value will not match the cost of repair, and there's a lot of liability to loose far more than you could stand to gain if it doesn't go smoothly. In spite of those finishes often being thicker than the top itself, in some eras of production I swear they laid the color right on the top, leaving no room to sand level and buff without going through.

You could also thin some clear epoxy with lacquer thinner and fill with that.