For the ssf, It depends what frequency your box is tuned at. Below the tuning freq., the sub unloads. If it's tuned pretty low, it's not as big a deal, but if it's tuned at say 40Hz or so, you risk damaging the driver if you play test tones through it.
As for the amp, the JBL's usually are underrated, so the 600.1 should be fine. I've heard some guys running them with 750 RMS, but 300 watts should be fine, especially if they're ported.
If I were you, I'd build the box yourself, but you can find a stereo shop, they'll usually build one for you. Check out
http://www.woodlawncabinetry.com/ He posts on caraudioforum.com and a lot of guys over there have gone through him. He makes great boxes and everybody over there is very happy with the results. His name is Phil and his screenname is MrCabinetry. Just ask him for a quote.
I wouldn't bother with a cap. Just upgrade the "magic three". Changing the wires from: battery + to alternator, Batt - to ground, and engine block to ground to 2 guage should solve any dimming problems you might encounter. With the 600.1, you should be fine, it won't put too much strain on the electrical system.