Prius III with JBL no Nav - eliminate the JBL system COMPLETELY

I'd like to eliminate the car's JBL components entirely - HU, amp and speakers - and install my own. I have a Pioneer AVH-P4400BH, an old school Soundstream D50 (for the fronts, the HU will power the rear speakers), a Sound Ordinance BT-8P woofer (not a true sub), and Infinity Reference 3020cs component speakers (front and rear). It seems to me that the best thing I could do is bypass the stock wiring to the JBL amp from the HU, run my own signal and trigger from my HU to the woofer and power amp (they'll be placed under the seats), run power leads (fused) from the 12V battery to the woofer and power amp, and then splice in to the appropriate 12V source in the dash for the Pioneer HU. I DO NOT want to cut any existing wires! For the speakers, I'd use the car's harness for the rears, and likely run my own wires for the fronts -we'll see how that goes. As for steering wheel controls, well, they'd be nice to have, but I really don't need them, so the PAC adapter is just a maybe.

How is my thinking on this?

 

I read Spiderman's (excellent) PDF's on replacing the dash speakers. That caused me to consider placing tweeters up in the dash (I was going to mount them high on the front doors), or getting some high quality 3 1/2 inch mid/tweeters (coaxes) and placing them up there. I'd put either 6 1/2 inch or 6 x 8 mid/woofers in the doors.