Oh sorry, I read too fast. Didn't fully read all your questions.
Yes, possible to produce a good cheddar with low sodium. Trickier, but possible, you can also sub in potassium chloride instead of sodium chloride. The reason it is tricky is that the rate of maturation is affected by the sodium content. Simply put, the degradation of fat and protein is slowed down by salt. Without as much salt, you need to slow it down by other means, such as by aging at a cooler temp. So for cheddar, if you drop the temp to 38F, and keep it at 37% moisture (on the drier side for cheddar), it should work.