What is the equation for capacitance with aysmmetric plates?
I'd consider using the microstrip model and then think of ways to develop it: -



Where the formulas quoted on this website calculator are: -





This is a starting point and I would urge you to look at other website calculators and compare formulas. There should be a site that gives a derivation of proof that might allow you to reduce the ground plane from being infinitely wide/long to something more akin to your problem.

The model above assumes an infinite ground plane so it will give a slightly higher value for capacitance.