Sorry, I'm late to the party.
OP, did you purchase your miniDSP product yet?
As a first step though, one should always try to treat the room first as much as possible. I know that sometimes there are design constraints, preferences, etc.. but some absorbing panels in corners, and/or on the walls disguised as paintings or pictures go a long way.
You can't correct a horrible room via digital filters. But small tweaks are indeed possible.
As posted, yes, you can use the miniDSP with Dirac as a DAC, and send that to your STA9. or connect your source to a miniDSP DDRC-22D, then to your DAC9/STA9 combo.
The Pi + BruteFIR would also work. More hands on and DIY approach than just following Dirac's instructions.
Another way is to use a real computer (those small NUCs are pretty cool) and JRiver. JRiver has a LOT of tweaking possible, including FIR correction via convolution. You will need tools like RePhase or DRCDesigner to create FIR filters. That goes digital out to your DAC9/STA9 combo.
Many ways to go about this, depending on your requirements, playing files from computers or CDs from player.
I have moved away from CDs and love the resolution and ease of use from HiRez files.