Electricity always looks for the easiest place to flow, so if the starter motor is engaged and the 12S battery is older so it can't store the original amount of energy, then the voltage drops to less than what the ECU and ignition need to function. The 14S battery simply adds lead and acid so that it can store more energy. Since it holds more it can generally age a lot longer before the capacity diminishes to the point where you have a problem. Since cold temps can diminish performance, the 14S is also better for cold morning starts. On a trivia note, batteries are sized for the electric system and it would not be good to stick a huge car battery in, because it would never get to fully re-charge and you'd diminish battery life.
Of course, your 8 AWG ground wire would improve starter performance. It's a fatter tube to flow more energy from the starter back to the battery. It's a good mod which can't hurt.
Love your attitude toward trying new things and don't want to rain on it but before others try adding capacitors, I'd encourage investigation. Capacitors dump their energy very quickly, so yes your parallel caps may give the starter a touch more snap initially, but then they too are a drag on your charging system. They also add a parasitic leak and each one introduces a new failure mode. In some high tech vehicles, capacitors are part of an engineered system to provide power, but these are far beyond what you describe. I've seen a lot of smarter people than me show how using the same weight penalty in adding battery size makes more sense for starting vehicles, so just installing the 14S battery would give you the same results or better. And it's easier.
