I'll make a simulation and let you know my conclusions. I really don't care if I don't currently have the knowledge to understand. I already invested too much effort. I'm going to understand it even if it kills me.The maximum voltage on the capacitor is determined by the comparator. I don't know where you got 1.45 from, but there are 3 resistors on the comparator that determine when it goes high and turns on the MOSFET, and that determines the maximum capacitor voltage. 1.45 isn't it, but it should be easy to figure out.
Beta is a parameter only BJTs have, not MOSFETs. Beta is current gain, and you can't have current gain when there is no input current.