I have asked them to book me with one or two instructors only for the sake of someone keeping (and hopefully caring about) track of my progress. However, I was told that this is best and their way of teaching is to switch instructors. I think they are just milking me and do not care about my progress. I am a quick learner and normally pick things up very quickly. What to do?
Being prepared to fly with two Instructors is reasonable. You have said that your school only employs full time instructors so this should be achievable. When a student is being taught by two instructors it is critical that each understands the standards taught and learned with the other and therefore each is clearly in tune with your progress. It is fundamental that there are no contradictions in standards from the instructors. The CFI/HOT should ensure consistency. You have a right to expects all this.
It is simple, they provide this to you or you leave and learn where they do. All the rest will then take care of itself. Most instructors do care and do a good job. Bad eggs unfortunately do it exists but they are easy to spot.