As you can see, I managed to rid the world of these artifacts. The idea is very similar.

1. Divide the 2d space into a non-uniform grid. If two lines are too close, remove one.
2. Pick a rectangle in random, check if it's been modified across axis-y (in height) and if it's direct neighbor was modified across axis-y. I both were not modified, have them renegotiate the segment between them (one will donate some space to the other).
3. Do the same as in step 2 only this time on the other axis.
4. Repeat the process until you modified as many as possible.

Non-uniform grid (1):

Negotiating on axis x (2):

Negotiating on axis y (3):

Result (4) :

As you can see, I managed to rid the world of these artifacts. The idea is very similar.

1. Divide the 2d space into a non-uniform grid. If two lines are too close, remove one.
2. Pick a rectangle in random, check if it's been modified across axis-y (in height) and if it's direct neighbor was modified across axis-y. I both were not modified, have them renegotiate the segment between them (one will donate some space to the other).
3. Do the same as in step 2 only this time on the other axis.
4. Repeat the process until you modified as many as possible.

Non-uniform grid (1):

Negotiating on axis x (2):

Negotiating on axis y (3):

Result (4) :