No horizontal cuts.
The idea of vertical and horizontal cuts would be a good one, if the curd remained in one place. But it does not, so this is unnecessary.
The curd is cut uniformly by stirring motion, which moves the curd around so that it is all cut. Trust me, it works
This is how I learned to do it. You stir first in a circle, then in a figure 8 pattern with some wrist motion to bring the bottom curd up to the top. It's very hard to explain, but not very hard to do.
Chetty's idea is a great variation of this same principal for a small vat. Though personally I would use copper wire or stainless steel lead wire (like you would use for fly fishing) and not polymer fishing line. But that's just my opinion
Or, you can go to a music store and buy some stainless steel guitar strings. Buy good ones, they are very high grade corrosion-resistant, acid resistant alloy that is annealed and can withstand a lot of tension.
The big cheese harps like we use have a copper tip, and are used in a round bottom copper vat. You let this tip rest on the bottom of the vat, and run it around. The curve of the bottom moves the harp up and down, helping to lift the bottom contents up to the top.