First of all, when you change a zero frequency, you should also see the magnitude of the loop response change, not just phase, which will also change fc. Are you taking this into account? Or are you simultaneously modifying some other parameter (like K) to keep fc constant?
To do your analysis, I would recommend forgetting about the circuit component equations for now and just directly define the pole and zero frequencies and K of your system. That's a lot more straightforward than modifying component values trying to recreate the same effect. Once you have pole/zero values you like, then you can derive component values for them.