Here's the model back with a fillet at the join, in case anyone else was following.. I scaled the model down by 100 times, twice, then put a .005 m fillet on the join, then scaled it back up to ludicrous! I also put a blend at the tip for grins. (Though I ended up with that last little non-continuous patch, for obvious reasons).

The OP should really just use a point as the edge up there. If a machine cut the edge sharp, I could probably apply the radius by licking it!!