For the horizontal cuts, try going to the dollar store and purchasing a cheap stainless steel skimmer. Bend the skimmer into an "L" shape with the skimmer part becoming the horizontal part of the "L".
After cutting the vertical cuts, insert the skimmer just below surface at the size needed (1/2", 1/4", etc.) Then sort-of twist the skimmer back and forth at that level to cut the cubes. After that level is cut, move down the next increment and continue until the whole pot is cut into nicely shaped curds. You can actually move pretty fast once you get the hang of it and they come out better than any other method I've tried. (It's actually a lot like the hanger method above but the skimmer has a nice sharp knife-like edge.)
When doing it this way, you could cut from about the center to the edge of the pot from top to bottom, then turn the pot and cut the other side the same way.
This has been the most successful way to cut the horizontal cuts for me. After that, I take the skimmer and lift curds from below to be sure they're all cut pretty close to the same size. Those that aren't I cut either with a large whisk or another knife.
When I look at the one you purchased on-line, it looks like it would smash the curds more than cut them... Has anyone else used one of those?