Reddit mentions of Chicago Electric Power Tools 4" Plate Joiner

You should let it be. Anything heroic you attempt now will just make it obvious you're trying to cover something. Embrace the work as it is. Then, next time, don't start with dimensional lumber that has been pre-radiused, [edges are rounded over]. Or, if you do cut off one edge and use that to mate to the edge of the 1x12. Then get yourself some clamps to pull the two pieces together - this will help close the gap. To align the tops of the two pieces, use biscuits [requires plate joiner - look it up] or a dowel jig. Then don't stain so dark; most woodworkers hate when you try to stain light wood a dark color...it looks sketchy, I am one of those woodworkers :-) Most of all have fun. I dig the design you came up with, clean and simple.