My modular board is currently the result of my third attempt to make one right. My modular tiles now fit perfectly together if cut out accurately.
There is only one way you can do it right:

Each square that makes up a walled-edge, has 1/2 of the wall's width intrude into it.
That super spangly HQ board uses a full square to space walls, but this lengthens hallways making the set incompatible with the Quest maps.

The point of building a modular board is to be able to use it exactly as if you weren't. If you have to make on-the-fly changes, you just created a constant pain in the ass instead of a cool-ass modular game board.
The Daria's husband (who I can only assume is named Trent or Tom) board is actually the better of those above, because the spaces align. However, it uses full-width walls against full-width walls, which results in the need for spacing additions being placed on the corners and intersections.
What I did was increase the size of each square (I reduced the size of some trappings so that boot laying around wasn't freaking huge) to 3cm. I also do not use erect walls, because they're just not fun at all, ever. They may look cool, but playing with them absolutely sucks. I made 3mm cubes into "end-caps" to represent single and double-blocked squares.
I spent a couple months figuring this all out.