I've repaired damage like this on my Kay. I made some thin spruce veneer on my table saw. Then used an X-acto knife to cut the broken edges straight, cut a piece of the veneer to fit, and glued it in.
A couple of times over the 40+ years I've had the bass, I had the top or bottom removed by a luthier friend, and took it home to fix the edges, and had the luthier put it back on. When I did this, I rebuilt the edges from the inside with large pieces of veneer on the inside, and corresponding smaller pieces of veneer on the outside. I did this in 3 layers which didn't exactly correspond with the layers of laminate on the bass, but it made a strong edge.
This is way too much work to have a luthier do and is tedious, but if you really care about the bass and don't mind putting in the time and effort, the results can look good.
If you look here:
http://www.billbentgen.com/bass/images/kay_top.jpg
at the top and bottom of the picture you can see the result. You can also see a chip on the top where I need to do it again. It seems no matter how careful I am with the bass or the humidity, this type of damage happens over time.
