If I were repairing that, I would use a hard marine epoxy like West Systems, reinforced by a little piece of fiberglass cloth on the inside of the cavity. I wouldn't rout out the wood.
Wipe some wax on the paint surrounding the crack, but don't get any in the crack. Then put a piece of wide masking tape over the area, covering the crack.
Now turn it over and work from the inside. Put some masking tape dams in the pot holes to try to keep out the epoxy out of the holes. It's not a big deal if some leaks in; you just have to clean it out with a file later.
Apply the epoxy from the inside. Dab some on the crack and let it sink down in. Keep adding more until the crack is filled up. Then spread some around and lay down the piece of fiberglass cloth. Spread some more epoxy on top of the cloth to get it saturated. Use a scrap of cardboard to smooth it down and keep it from being too thick.
As an alternative to the fiberglass cloth, you can cut and fit a thin aluminum plate, and epoxy it down inside the cavity. That will reinforce the whole controls area structurally, plus provide some shielding and grounding.
After the epoxy is cured, pull off the tape on the outside. The epoxy should have filled the crack right up to the surface, and hopefully didn't ooze out anywhere. From there you can lightly scrape it smooth and touch up the paint, or just leave it as a thin "scar" line.
Did I mention that you should do this operation on top of a sheet of waxed paper? Epoxying your bass down to the table is embarrassing. I've done it.