Can Room Correction Be Added to an Existing DAC?

The MiniDSP SHD Studio is a much more modern component, with much better quality internals than other MiniDSP products. I would say say hardware wise the Paradigm PW Link is in a similar class as the MiniDSP 2x4HD. The SHD Studio is in a different league altogether.

Dirac and ARC are generally considered to be similarly good, with many people giving a slight nod to Dirac. I believe Dirac is much more flexible, allowing you to tweak the target curve to suit your needs exactly.

minuDSP does include Bass management upto 2 subs which is very flexible, but the Bass management part has a steep learning curve.
The benefit of a sub with good speakers is not so much better/deeper bass output, but more of flexible positioning to reduce room modes. I would recommend getting a UMIK-1 mic and downloading REW (a free audio analysis software) to measure your frequency response first, before deciding if a sub is needed.

Most people/rooms benefit from multiple bass sources, so room modes cancel each other. However, In my case my speakers when measured individually are quite flat, However when I measure the combined L+R response with a mono signal, I have all kinds of peaks and nulls in the bass region. Adding a sing sub, introduced some crossover anomaly but restored a flat bass response. With a little tweaking of the crossover, my overall combined response is now fairly flat.

Look into DSpeaker line of products

As many others have said, you can add a digital signal processor in front of your DAC.
Dirac with miniDsp is probably the most cost efficient solution. If you want to evaluate Dirac you can download a time limited evaluation installation for Windows or MAC.
I tried it and the effect is not mild. The balance achieved is an improvement bot overall I didin’t like that the stereo image becomes too wide, to an extent that I lose the central image.
Also, I own LS50 and tried the Acitve DSP-ed LS50w. I didn’t like the result. I think some detail is lost in the processing.
Try before you buy.

Also, bass modes you can’t fix completely with DSP. You can enhance in one spot to a certain extent. The best solution for that is multiple subs, minimum 2 optimum 4.
There was a company that sells time alligned set of 4 subs. You place 2 on one wall the other two at the opposite wall. When the wave of the front two reaches the rear wall, the rear pair of subs fires a wave in counter phase so that it cancels out the reflected wave. That virtually removes the rear wall and the wavelength can fully develop as if in empty space. To my knowledge that is the best solution for bass. You could ameliorate with room treatment but that works better for higher frequencies with shorter wavelength.