The big three upgrade is something i would recommend to anyone who is running 1000 watts or more in the vehicle.
4ga. is 'okay' for 1000 watts......but it is better to have at least 2ga. or 'do it once' and run 1/0awg
You do not need a HO alternator for ANYTHING you have mentioned......additional batteries are warranted before a new or additional alternator and you dont even need an additional battery to run any of the forementioned setups.....
An equalizer is not going to really help you all that much in the bass department.....it is more for tuning out the response peaks or dips across the rest of the frequency range and not so much for 80hz or lower........if you are wanting to add some depth and ouput to your low end bass you should really look into an Epicenter or other bass enhancement unit......the Audiocontrol Epic 160 is an amazing unit and is what i use alongside a Kicker KQ5.........they are a little pricey however.....but Hifonics and Power Acoustik both make decent quality epicenters as well along with numerous other brands............
also 3 10" lower power subs will not neccesarily be better than 2 12" high power subs.......lots of variables come into play but thats my opinion
And as for the BRZ1700.1d......I was referring you to use that with the Pioneer subs that you mentioned.......however amazingly after quickly looking over the specs it seems that that would be a good matched amp for all of the subs you have mentioned........
with the 2 memphis subs you have now.......wire them like this for a 4 ohm load and the amp will supply 300 watts to each subwoofer into 4 ohms.....
Subwoofer Wiring Diagrams, Two 4 ohm Dual Voice Coil (DVC) Speakers
which is perfectly fine....yes i know that the rms is 250 but it is generally a good practice to overpower your subwoofer, and really any speaker component for that matter, by at least 20% if not more......the reasoning behind that is to essentially get all of the output possible from your subs without pushing your amp into clipping to do it.....make sense? believe me....clipping your sub signal is bad bad bad and will ruin speakers quick.....give them a nice toasty smell lol
and with the 2 alpine 12's you can wire them like this for a 2 ohm load and the amp will put out 600 watts to each sub into 2 ohms.....BUT that is if they are dual 2 ohm voice coil subs....forgot if you said which they were....if they are dual 4's than scratch that......
and with the two pioneers you can wire them for a 1 ohm load if you get dual 4's and the amp will put out 1050 watts into 1 ohm......
hope that helps