The cutter that I used to make the horizontal cuts is based on the design discussed here:
http://cheesemakinghelp.blogspot.com.au/2013/11/making-horizontal-curd-cutter.html and in replies 5 and 7 here:
http://cheeseforum.org/forum/index.php/topic,13102.msg101584.html#msg101584Mine seeks to improve on these designs in a a couple of ways. First, the materials in contact with the cheese are stainless steel. The vertical rod is 5/16" diameter, with grooves machined into it at precise 1" intervals--more about these in a minute. The thin horizontal rod is a piece of 3/32" stainless TIG welding rod. (I considered using 1/16" rod, but it seemed like it might not be quite stiff enough.) The horizontal rod fits through a hole drilled in the vertical rod; this fit is a loose sliding fit, so that the two can be assembled and disassembled easily. All of this allows the key pieces to be put in the dishwasher and to be sterilized in boiling water before use.
Second, the hub through which the vertical rod passes is machined to allow indexing of the rod for 1", 1/2", or 1/4" horizontal cuts as desired. This hub should be made out of stainless also, so that it too can be tossed in the dishwasher. Unfortunately, I do not yet have any stainless on hand of a suitable diameter, so I made this one out of mild steel; I will replace it down the road when I acquire the appropriate material. Another option would be to make this hub out of a food-grade plastic ... but again I don't have any of suitable size on hand. The hub is machined to 5/8" diameter over most of its length, with a flange of 1" diameter; there is a 5/16" diameter through this hub. The 5/8" diameter is cut with 4 slits, spaced 1/4" apart; the slits are deep enough to intersect the 5/16" hole by about 1/16" of an inch.
In use, this hub is set into a wooden cross piece sized to fit over the pot. There is a 3/8" diameter hole drilled through this cross piece, through which the 5/16" rod passes. There is also a 1" diameter hole counter sunk to accept the flange of the hub; the counter sunk is drilled to a depth that leaves the hub just sitting proud of the surface. As can be seen in the pictures, this allows the hub to be secured firmly to the crosspiece with three screws and washers, but also easily removed for cleaning.
The final key element of this design is the set of four hitch pins modified to fit on the hub so that the straight leg lies in one of the slits in the hub, and the bent side clicks in place on the round side of the hub. These hitch pins engage the grooves machined in the 5/16" diameter stainless vertical rod. Since the grooves are machined at 1" intervals, one can index the rod at 1" intervals by inserting one hitch pin into the hub. To get 1/2" indexing, insert two hitch pins in the 1st and 3rd (or 2nd and 4th) slit. To get 1/4" indexing, insert all four hitch pins.
To cut the curd, the cutter is assembled minus the hitch pins; the cross piece is set over the pot, and the cutter is let down through the curd until it hits bottom. The desired hitch pins are then inserted into place. The handle is used to sweep through 180˚; since the cutter extends to both sides, this will make a complete horizontal cut. The rod is then raised until a hitch pin clicks into place, indexing it and holding it so that the cutter can be swept through another 180˚. The rod is raised until the next hitch pin clicks into place, and the process is repeated. Even when indexing at 1/4" intervals, it takes very little time to complete all of the horizontal cuts.
I experimented with making the horizontal cuts first in my previous swiss make, and found that that does not work as well as making the vertical cuts first. The problem is that the weight of the curd tends to press it back together before the subsequent vertical cuts are made. By making the vertical cuts first, there is enough room, and enough whey starting to be released, to allow the cubes to move a bit when released by the horizontal cuts.