Sorry to be that guy, but theres a lot of not so great info in here. More so just generalized regurgitated **** that someone read and pieced together from various forums.
1) A DSP does not make anything sound better or worse (see below)
2) compressed or uncompressed files don't even belong in this discussion. Not even close
3) even with passives, a dsp will be a GREAT improvement over a head unit on its own
4) rear speakers do not negatively effect staging/imaging/tonality/impact/dynamics when done right. People saying "toss them" are the same people that are reading and regurgitating and their recommendations should be taken with a grain of salt
5) signal delay on left vs right is the most important, especially considering that you are new to this. At higher frequencies, phase/timing isn't that important, amplitude is. I am willing to bet that you OP, as a newbie to DSP's and tuning, wont even notice much of a difference in going active vs passive on this setup with a proper tune UNLESS something is out of the ordinary that requires a lot of tuning work. doubtful on that last part though. For your situation, set signal delay to the midrange drivers, take your measurements and do your eq and use the RTA to verify that the mid to tweeter crossover is in phase. do this by swapping tweeter polarity at the crossover and compare measurements. Im actually making a video on verifying phase cohesion as we speak, but i messed up my screen recording so i have to re-do it tomorrow
That said, a DSP on its own does nothing. Its what you can do with its features that make the difference. Cheaper processors are usually ok if you are using an aftermarket radio, and arent trying to dive to deep into what is possible. In your case, something with more robust EQ is going to give you a massive improvement on its own IF you know how to utilize it properly. Yes, even with passive crossovers. From there, you can ditch the passives and you can adjust timing and crossovers on the mid to tweeter separately to get better phase cohesion.