Getting a single feedback peak from a basic 4 stages phaser
If I follow the OP’s description properly, the description is what would be a comb filter, given the all-pass filters operate as delay lines (over a certain frequency range of operation). The sum of a signal with a delayed copy of the signal would be a "comb" response, that would cyclically go between constructively summing and cancelling since the phase through a delay line is linearly proportional to frequency (so cylces between 0° and 180° as you sweep frequency). To eliminate the second peak, the bandwidth of the delay line or the feedforward path from the input that adds with the output would need to be limited.

To achieve what is wanted, consider a simple IIR filter with pole placement at the resonant frequency, given by :

$$H(z) = \frac{k}{(z-\alpha e^{j\omega})(z-\alpha e^{-j\omega})}= \frac{k}{z^2-z2\alpha\cos(\omega)+\alpha^2}$$

Where $\omega$ is the normalized radian frequency of the resonance and $\alpha$ sets the bandwidth of the resonance, and $K$ sets the gain. Use $\alpha&lt;1$, with the closer it is  to 1 the tighter the resonance.  

For example, with $\alpha = 0.99$, $k=0.1$ and $\omega = 1$ the response is: