You had asked what else would work. I have had great results with Titebond III, and I understand that they now have a stainable version.
Stainable or not, you can put a bit on a thin piece of wood, and force it down into that crack a bit. Then, as with the CA, compress the heck out of it with surgical tube or bicycle inner tube. Should close down, forcing the excess out. Clean the DRIED excess carefully and you may not even have to refinish. Hide glue will work if you can get it thin enough to force into the crack.
Not the end of the world, for sure. You've got a nice piece there.