Can I increase the resistance of my linear potentiometer?

You need a stable voltage across the potentiometer else you will get a lot of noise on your signal. In normal circumstances you would use a capacitor across the pot - but you cant here as you are switching the supply. So make sure the voltage has time to stabilise before you take the ADC readings.

In this circuit I dont see any real benfit from using a MOSFET rather then the transistor.

Make the settings for A0 and A1 the same, and your pot reading is just A1 / A0. Not really complicated.