I am not sure that heating the cheese faster or slower would have that much difference. In my experience, drier cheese has more to do with pressing time and pressure. I would try pressing with less pressure first and see what difference that makes.
Homogenized milk is more difficult to curd so I would not use that. If you used skim or 1% milk, you could try 2% or whole. I would stick with non-homo if you can get it.
Let me know what you find out.