I found my best litter, box, liner combo!
 

It has been two months since my last post on this subject and some of
that text describing the setup is repeated below. I just want to
update that it has been five weeks since I last made a complete litter
change and the box, liner, and litter look like what the old setup did
after a week (I've put in a bit of fresh litter every 1-2 weeks). The
key is that I put the liner on better than the first time at the time
of my initial report and there are absolutely NO seams inside and NO
folds at the front or back to catch any urine. Probably work even
better if I can get a scoop with small openings to catch even the
smallest pieces of used litter.

Anyway, here's the description of the setup:

Tidy Cats Litter Box (see web site) with high back on the bottom and
hinged front on the top for easy access. The high back means unine is
no longer being forced between the seam as it has on other covered
boxes.

Tidy Cats Jumbo Liner which the bottom fits into neatly leaving a
distinct lack of folds to catch urine and prevent it from reaching the
litter, while still being loose enough to allow a trick described
below. A complete replacement of liner and litter is accomplished by
turning the liner inside out as one removes it from the box.

World's Best Cat Litter for its well known attributes.

I can peel clump off the back of the liner by carefully inserting the
scoop between the clump and the liner and flipping it forward in one
piece.

On the somewhat looser front, I can grab the liner where it emerges
from under the top and flip the clump off. You can't do that with the
box, so that's why I like liners.