Filter design with 8-tap latency on recursion
This is tricky. Any filter with 8 tab latency between coefficients can be represented in the z-domain as a rational function in $z^{-8}$ . That's basically the same as saying the impulse response has 7 zeros between each non zero tap. Any filter with this property is periodic in the frequency domain. You can pick any transfer function from -pi/8 to pi/8 but the regions from pi/8 to 3*pi/8,etc. will just be repetitions of that.

You may be able to do better with varying delays but this is a complicated design problem