Audio system overhaul help

I'm designing my audio system overhaul, and I'm new to everything car audio so I'd like a sanity check to make sure I'm thinking of everything correctly.

I have a 21 Tundra, non-JBL, with factory amp. I really am just concerned about the front speakers and a sub. I have an

$165 Alpine MRV M500 - Alpine Monoblock 500W RMS V Power Series Car Amplifier

Alpine MRV M500 amp with speaker level inputs and pre-amp outputs, and am thinking about the Kicker hideaway 8 amp/sub combo for the sub. Also have some kicker component speakers with crossovers.

The hookup I'm thinking would work like this: Mount the Alpine amp under the passenger seat, in place of the factory amp. Run the speaker input wires into the amp at that point, since it has speaker level inputs. Hook the speaker output back into the rear speaker wires directly, and then into the crossover inputs on both front sides. This would then feed the component speakers in the front.

After that, the pre-out jacks could be ran to the hideaway amp/sub combo, which would run the sub. Power coming off the battery and split to each amp. Running a 4 gauge wire, would that be enough power?

I know it's hard to describe in a post, but does that seemingly make sense? Appreciate all the feedback!

 

I just realized the

$165 Alpine MRV M500 - Alpine Monoblock 500W RMS V Power Series Car Amplifier

Alpine MRV M500 is a mono subwoofer, so I'm not able to use it for the component speakers... Recommendations on a different amp? Or has anyone kept the factory amp, and just added the sub and speakers?