Good Morning Amneet Ahluwalia,
You have pretty impressive setup in your car buddy. As far as price is considered the install should have cost you around 1lakh. And after spending this much when you don't get the desired SQ then it's something you seriously need to look into.
My first question - Why all products are from Polk? Didn't you consider other brands like Rainbow, Gladen or Hertz?
Head Unit: Pioneer AVH-X8590BT
Excellent SQ HU from Pioneer. Doesn't have TA but you don't need TA and it's for audiophiles who require the best possible SQ that can be created. Even without TA your setup should have very high SQ levels.
Front Door Components: Polk Audio MM6501
Very powerful Component with 125w RMS rating. I don't think MM6501 has anything thing to do with low SQ in your setup
Co-axials (6x9): Polk Audio MM691
Again one of the most powerful 6X9 coaxials out there with 125w RMS rating. I don't think MM691 has anything thing to do with low SQ or bass in your setup. It should actually produce some mind blowing bass. I am quite amazed that you don't even find any bass from these speakers. My car has DB6501 components in rear and it puts out lots of bass. Heck when my rca cable to my amp which gets connected to subwoofer got disconnected it took me close to 2hrs of listening to notice a small amount of bass reduction from my setup as subwoofer was not working. So your speakers should ideally produce lots and lots of bass.
4 Channel Amplifier: Polk Audio PA660.4
A bit underpowered for you setup. 75w RMS X 4 at 4ohm and both your speakers are rated at 125w RMS . Wiring them at 2ohm load won't do much help i guess at i has only 85w RMS X 4 at 2ohm rating. Infinity kappa 4 with 125w RMS X 4 would have been a perfect match. But i don't think this amp is cause of low SQ and bass in your setup. After all its a class A/B amplifier so should ideally produce a bit more than rated power.
Mono Channel Amplifier: Polk Audio PA880.1
A very powerful monoblock amplifier. You have invested in such a good amplifier which has 500w RMS at 2ohm and 800w RMS at 1ohm (dynamically). As your subwoofer is rated at 360w RMS at 4ohm i am assuming your monoblock is wired at 4ohm load now and produces around 300w RMS. IMHO monoblock are quite crappy to hear at 4ohm load. Its always better to wire monoblocks at 2ohm or the best is to wire them at 1ohm load.
Polk Audio DXi112
Throw these away immediately. I am sure this subwoofer in a basstube is the major cause for low SQ in your setup. Get 2 Infinity Kappa 120.9w 12" subwoofers and wire them to 2ohm or better 1ohm load. Also you a sealed box. You should have tigh fast punch. 120.9w is one of the best SQ subs around and should cost you 15k for 2 subwoofers.
Wiring Kits: 2 Pairs of Kicker 4 AWG
Nothing to worry but seeing installers stupid advice of replacing a powerful 6X9 with components i suggest checking the grounding of amps and also a general installation of overall install too if possible. Also a 1 farad capacitor is advisable if monoblock is wired under 2ohm load.
Hope this help.