What follows is how I would tackle it:
You appear to have quite a bit of tape or glue residue on the stock. Did you put a release agent such as paste wax on the stock prior to gluing? The glue doesn't usually bond tightly to the finish and can likely be picked or pushed off. How do the edges of the break feel? If they feel smooth, you should be able to touch up the edges of the break with some light walnut stain and then touch up the finish with a bit of Truoil or Linspeed (if you can find it). If they are raised, you might be able to to smooth the edges by lightly burnishing with something like the side of a chrome plated screwdriver. Whatever you use, make sure it is dead smooth and don't use so much pressure that you dent the wood.
That break in the plate is pretty much what I would want to see if it were mine and it was broken. It is V shaped, which should help with alignment, and there is a lot of surface area for the glue to bond to. I would start by removing the plate, cleaning up the end of the stock and applying a heavy coat of paste wax. The break is jagged, but looks like a clean break. Try not to dislodge any slivers or disturb anything. Put the plate back on the butt and test fit the pieces. You are good to go if the fit is good. If something is holding the pieces apart, it is likely a dislodged sliver. You will need to find and remove it or them. Dental picks work well here. You are ready to glue when the parts fit well. Make sure you know how you are going to clamp it before gluing. Don't cheap out on the glue. Do your research and choose the best adhesive for the material. Based on my BRIEF research, Locktite # 380 appears to be a good choice for gutta percha.
Hope this helps