In my experience, which is fairly limited, a front to back split is often terminal. However, I agree, open on the crack as much as possible to get glue in. If you know a nurse/doctor/intravenous drug addict, I suggest you use a syringe and needle to get glue as high into the split as possible. Use a PVA glue as others are too brittle once set. I use sash clamps though a vice would be good too and leave to set for 24 hrs. Dowel with fluted dowels as these allow glue to surround the dowel and give better adhesion. Once set rub down and leave for another few days before you apply linseed oil. Leave another few days then tape up. Good luck.