I agree with Eric on his points. I think you should be able to run the mini-dsp from the second set of pre outs.
I would highly recommend finding an external linear power supply with a good size capacitor bank. The mini-dsp comes with a wallwart, which is adequate, but you’ll sacrifice sound quality for sure. Since your going to use this as a subwoofer DSP, the power supply size is very critical to allow the mini-dsp enough constant voltage to properly build the large bass waveforms. If cost is an issue, then I would look at the standard 2x4 (non HD) model. The 96khz high-resolution and FIR filters of the HD version are nice-to-have, but I would rather have a large linear power supply instead of these features. The standard 2x4 model still has crossover / parametric EQ / time delay.
The Dirac Live is high end automatic room correction that is similar to stuff like Audessey but more complex and allows some tweaking. I have used Dirac before, but I could never get it to sound right in my opinion. It does weird things to the sound phasing and the bass correction will sometimes over EQ the subs to the point where the woofer peaks.
In my experience, if you feel you are lacking bass in certain frequencies, you are better off doing acoustic treatments. Look into getting a couple of GIK Acoustics Monster Bass Traps with the FlexRange RANGE LIMITER feature. Stick them in the back/front corners or line the back wall. I have used these and they are effective in improving bass response in a room. Make sure you get the FlexRange RANGE LIMITOR option.