So you're doing ~1200 with the Cadence, ~1200 with the SQ and ~500 with the PPI??
No idea what your impedances are, but no matter how you slice it, that's a ton of power.
It doesn't make any sense to me why people always want to go straight to the batteries in a situation like this.
The issue is clearly the alternator. At low-moderate volume it's not surprising the alt performs fine. At high volume you should be seeing 12.5-13v a lot of the time -- still plenty for things to run fine in the short term.
Long term - your alt isn't going to last long UNLESS you're someone who RARELY blasts it.
Do what you want to do with the batteries -- looks like you have a logical plan with that, but assuming you like to turn it up occasionally -- you need to be HO alt shopping. That degree of current demand will generate a LOT of heat and the alt's life will be drastically shortened.
At 1500w my 130A ford alts were burning up every couple years. And I don't blast it very often.
That must be a very rare alternator. I'm not seeing a 140A replacement for that car, just the usual POS 105A.