Ya, that alternator is more than enough for your system, do your underhood grounds with some big cable.
The only advantage of a capacitor is with subwoofer amplifiers, which show your electrical system sharp spikes of power consumption, so rather than showing your charging system a 0 amp draw, and then a 60 amp draw all of a sudden, it shows it a constant 40 amp draw. (just made that number up, i just mean it shows a constant recharging draw, rather than the actual spikes of the amp)
A battery with a decent cranking amp rating is all the capacitance you should ever need with your current setup, tho.
In your current situation, my number one suspect would be a bad ground on your system or your cap. That would show your battery and your alternator a constant current draw, depending on how bad the connection is, which is ******* your battery dry, and putting a constant load on your alternator, and then when you have the amplifier's spikes on top of that is causing your flickering or dimming.
A bad ground up front would most likely cause starting issues, it seems like your problems are primarily while using your system, which is why i suspected the issue is near your amps/equipment.
It could also be a bad cell in your battery. This would show your alternator a constant draw, since it thinks it need to recharge that cell, so it's constantly making it's full potential, and it's just terminating in the bad cell, which can't charge.
Have your battery tested at autozone or advance auto parts, and double check your ground connections in the rear. It's definitely something strange, tho, you'll be fine without the capacitor once you figure out what it is.