Phase Shift Oscillator | Theoretical Frequency Mismatch
You have ignored the effect of R1 and the input resistance of Q1. The parallel combination of R1, R5, and Rpi should equal R. In this case a lower value of R will help make this possible.

The formula for Fo is too simple to be believable. You don't provide a source or derivation, but I think it could only apply to N independent phase shift networks and here the three RC elements interact. The first is affected by the loading of the other two, the second is affected by the source impedance of the first and the loading of the third, etc. To create a correct formula you would need to derive the third order equation for this network and solve for F where the phase shift is 180 degrees.