What you're then describing may be perfectly normal as it's designed to cycle on/off depending on AC system pressures. It will do that more at times than others due to outdoor temp, interior temp setting, etc.

I'd first get a second opinion as to its freon charge and the ONLY way to do that is by having the system recovered with a freon charging machine that recovers and weighs the total freon charge. By doing that, the tech knows exactly how much freon was in the system. If it's less than 1.65lbs, it's low and needs to be topped off (it's leaked from somewhere STILL or wasn't fully charged before).

Now, despite any stories you might have read, if the charge is correct, the AC blows cold at max cold settings then it's functioning correctly as designed. Throwing parts at it will only cost you more money and solve nothing.