I will agree with you that you cannot get quality 5.1 surround sound with only $300 worth of car audio gear. But you are comparing apples with oranges.
Let's say there wasn't a power issue and you could plug your system directly into the car and place the speakers around the interior and the subwoofer in the trunk/hatch. First, you would notice that there is a huge gap in sound between 80-200Hz where the satelite speakers simply cannot produce sound. Now pull out onto the road. Once up to speed your subwoofer will be come one with the road noise and will barely cut through. The small driver might shake your house but in a car all of it's sound will be drowned out by the road and absorbed by the interior panels, carpet, and headliner. In your home the bass can bounce off the walls, ceiling (and possibly the floor) creating full boomy sound. Not so in a car. If installed in a trunk, the sound will barely make it through the rear seat. Furthermore, the sub is designed to handle a wider range (usually up to 250-300Hz) and if it is installed in the rear of your car it simply won't project and all male voices and bass instruments will get pulled to the rear of the car and sound as if they were behind you.
Ok now about the power issue. AC and DC power supplies are two completely different breeds. You said it yourself that there simply isn't a way to power it. You might be able to find a way but there is no way the music will be as dynamic as using a 12v native amplifier.
And how about power ratings? You said your system is 500w. Is that 500w RMS? More likely max power. How much distortion do you have to send the speakers to actually get 500w? I doubt the satelite channels on the amplifier are much better than the 10-15w you get from a factory head unit.
And then you have the speakers. I already mentioned they probably can't play much below 150-250Hz. A car audio 5.25" speaker can play down to 100Hz easily. Upgrade to a 6.5" or 6x8" speaker and you won't have any problems playing down to 70Hz. The result is full range sound from your satelite channels.
With the satelites playing the bulk of your music/sound the subwoofer only has to handle 20-80Hz. Car audio woofers are optimized for this range with large voice coils, strong baskets, and long excursion motor systems. They can and will play 20Hz. Try popping out a 20Hz sine wave on your current system. If you're lucky it will burb at you and then go silent.