How to eliminate a gap of an offset in a corner
UPDATE: Attempt Number Two.


Okay, everything's set up almost like your first uploaded image:


Stone Gray 1x2 jumper plates as the base is the same.
The three Black 1x1 Bricks are still in those key positions, except they're all modified Headlight Bricks, instead.
All bricks have been skewered through with a combination of Light
Sword Blades and Shafts.


LEGO Digital Draw won't allow placement of a brick on a stud-less surface.  To get around this I used 1x12 and 1x6 plates for temporary
staging, and then deleted them after the shish kebabbing.


There's still a gap, but the gap number has been reduced to one, and
made less noticeable.





Let me know if anyone wants the build file (Minus Picasso's Junk Lighthouse behind it.).