I'm familiar with all of the equipment used but was not thinking about adding, but supplanting; I'll get to that in a bit.
I'm guessing that the system is extremely bright and very midrange heavy and lacking midbass (as noted), but not because there isn't any.
There is too much duplication of the midrange to high-frequency output, and the midbass cannot keep up.
The "Z" series coaxials are decent speakers; the tweeters are quite bright when left to their own devices, but they are good speakers.
6 x 9s are decent, but again, their full range, along with the other Pios, should be fairly decent.
But then you throw in a pair of those 6.5" pro-style mids in the rear doors, and you now have 4 mid-ish midbass drivers and 6 midrange drivers (4 of the same general output and 2 with exponentially higher output on the same wattage), 6 tweeters, and 4 super tweeters.
The system is entirely out of balance.
Now the fun part... budget.
There is no cheap fix here—not an arm and a leg, but maybe more than you were considering.
Here is what I would do to improve the sound exponentially.
Using one of the two GM-DX874s for the rear setup, put the Pioneer coaxials in the rear doors and replace the 6x9s with a 2-ohm 6x9 from CDT (or even a 4 ohm 6x9 that is strictly a woofer, not a full-range setup, or anything that you can afford).
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There is a seller on DIYmobilaudio that has a used pair for $150 us, might be easy enough to ship to CA if you cover the cost difference. I'll try and DM you the URL.
Even these as fairly efficient 4-ohm units running off about 100 watts from the pio amp, great option too.
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Using a 2-ohm 6x9 woofer in the rear would give you 150 watts x 2 to the 6x9's and 100 x 2 to the 6.5's, a nice balanced ratio in favor of midbass.
In either the CDT or that Rockville, you would set the 2 channels for those drivers as an LP filter around that 500 Hz mark on the amp to ensure they are only playing midbass and lower midrange, much better. Use the HP at around 60-70 hz for the coaxial in the rear doors.
I'd also replace using the LC1i/LC2i combo, a bit of a convoluted way to get this done, assuming you're using the output on the rear 4-channel to feed the subs on the GM-DX871.
If you're not opposed to learning a bit, then getting an entry-level DSP from Taramps would be a great option. Using the single LC2i to feed the RCA inputs on, say, a Taramps Pro 2.6s to configure all the non-subwoofer drivers and splitting the output off the LC2i, running one set to the DSP and the other to the subwoofer amp, then you could control all 6 channels, front and rear, for volume, time alignment, and frequencies.
QUBED makes a decent 5-channel non-DSP/LOC that is decent enough as well.
Up front, to match the rear coaxials in tone, timbre, and output, get the matching set of pioneer "Z" series components; even better, get the "ZCH" version, as the passive crossovers are much better than the standard "Z" components.
These are good:
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These are
much better. Bigger woofer motor/magnet assembly, better power handling, and a far better crossover that lets you run the tweeters at flat, +2 or +4 db.
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Mount the 6.5's in the doors and run the tweeters in the factory locations in the pillars.
This will completely reshape the front stage, bring it up closer to ear level, improve dynamics. , improve the imaging, both R/L and spatial.
I would bridge the remaining Pioneer and feed the Pioneer components up front with that remaining amp at 300 watts x 2, bridged, turning the gains down so that it's closer to around 175-200 watts x 2.