Wire won't help with box rise. 12g is fine for short runs to the subs...I'm running 8g for sub wire (and it's way overkill for the3k I'm running) but that's only because I had it already, otherwise i would be running 10 or 12g copper depending what the shop had cheaper
Box rise, more accurately, impedance rise, is the reactive load changes the woofer exhibits at different frequencies and it will happen, it's normal and you cannot mitigate it so don't sweat it. Resistive load can be minimized with all the other stuff you are talking about such as adequate gauge wire, parallel grounding, etc. My subwoofer leads are 12 gauge and at 6ft, way overkill, 16 would probably be adequate for the 1590 watts they could potentially carry. Get the largest gauge the leads will accomodate.
This 10 gauge OFC is a pretty decent buy and if the runs are less than 5 ft each, will cover it.
I have 10 ft of this lying around and will be using it next but it is redicoulsy large (think small garden hose) and connections require a bit of finesse. And as others have stated, only using it because I got it!