It's probably not that the 6.5" is garbage. In an NSX the factory enclosures are removed, a door plate is slapped on an uneven door surface, and the woofer is expected to perform with a 2" opening directly to its side. So what happens is the front wave and the back wave of the woofer meet, the bass cancels, and you get a 6.5" woofer playing upper midrange. Something a 2" dome can do. This is standard NSX installation. Then of course the sub is necessary, and if you were to measure you'd see this huge gap between say 80Hz and 300Hz, with the system producing virtually nothing there.
Now power that up by a 10 watt head unit (trust me it is no more than that clean) and of course you will get shitty sound. So the "upgrade" is then no more than a cool looking head unit in the dash.
So look, if it was me, I would yank those door speakers out. An NSX should not be using a 6.5". I have a 4" right now and it puts out 3x the bass of a high end high powered 6.5".
The NSX is loud. You need amp power, especialy wit a targa. You say you don't want to spend $300, but you need a 4 channel amp to drive all these speakers and the sub. The NSX cabin has little room and the electrical system is not the most robust for this kind of thing (small battery, small alternator). Cheap gets you a class AB amp at 40% efficiency. You get a big heavy amp that turns all the juice it sucks out of the car into heat.
You need a class D amp. That's 80%. Less size, less heat, less weight. But not less money.
So here is one I recommend:
http://www.sonicelectronix.com/item_40254_NVX-JAD800.4.html
small, light, with adequate power.