Finding good feedback coefficients for basic reverb
I don't know how to easily calculate stability criteria for your reverb topology, but it is easy to check if a set of delays and weights will give a stable filter (unless it is marginally stable or marginally unstable) by just calculating the impulse response and seeing if it blows up.

The easiest way to tune the reverb would be to use global optimization like differential evolution, where you actually try different delays and weights and optimize them against some cost function. The cost function could be such that it calculates the impulse response of the reverb and penalizes for instability, calculates the discrete Fourier transform (DFT) of the impulse response to get the frequency response, using fast Fourier transform (FFT), and rewards for something like spectral flatness. 

It's a moderate amount of work if you are not familiar with those methods.