Some speakers, like my Focals use hexagonal wire, which is the best. Flat wire is a close second. Flat and Hexagonal wire winds into much more tightly packed coils. Hex wire is best because the wire is close to being round, and it still packs well, but it takes very high precision coil winding especialy for more than one layer. Flat wire doesn't have to worry about getting the next layer exactly in the right place, because the previous layer is flat, but the flat wires don't carry current as efficiently for their weight as hex or round wire.
In addition to the tighter packing, hex and flat wire can make it easier to make the coil very precisely, so the magnetic gap can be made a bit smaller since it doesn't have to allow for so much variation in size, iving the speaker a stronger magnetic field to work with.
Lots of little things can add up, which is why expensive speakers are worth paying for.
As for the earlier problem about 600 watts at 2 ohms burning up your speakers, actually not. Usually, speakers are not burned up from having too much amp, but too little. If you listen to the speaker with non-distorted music playing, you can tell when it is getting close to having trouble and turn it down without hurting it. But when the amp is running out of guts and starts clipping, in a few moments you can get the voice coil really hot. The high frequency hash created by the clipping can't move the really large woofer quickly enough to create mechanical motion, so voice coil heats up instead.
I would recommend getting a good Class-d subwoofer amp. It is really helpful to have a sub amp that is incapable by design of any high frequency hash. Most class-d amps cannot go past 250 hz, which gives them plenty of headroom for a sub that is going to be crossed out at 55 hz or so. They also use power more efficiently. I wonder if you don't have enough juice flowing to your system, which would cause clipping when you are really cranking the bass. A class-d amp may be so much more efficient that you don't have to rewire the power and still get the levels you are looking for.
But because it doesn't have a huge xmax, it is about 4 db more efficient than most car audio woofers. Woofers with large xmax don't have as much of their total voice coil length in the magnetic gap. So they have weaker motors than woofers with less xmax. THey also have heavier voice coils, which also adds to the frictional losses -- you have to have a stiffer surround and spider to hold up the extra weight and thus more energy is wasted warming up the spider and the surround.
This sub, while not really high on xmax has some really good features. For one, it is NOT dual-coil. You don't need it, just power it with a single mono sub amp, which lowers the costs (and as you now appreciate, has less to go wrong). The frame is cast aluminum and the woofer is a stiff but light aluminum cone. It has a really robust spider and surround. It is optimized for accuracy, but if you want to go ported it has a slightly less-accurate sibling at the same price that works well in a ported box.
about $190 including shipping
Power handling: 500 watts RMS/800 watts max
SPL: 90 dB 2.83 V/1m
It has a 10" brother, about $40 less. It requires about a 1 cu ft box, but is less efficient. My 12-inch sub of the same series is mostly loafing in my car, so the 10" would be pretty good.
I really like my Profile Baja only $95 with shipping 300watts + rms from millionbuy.com
I looked up the power acoustic subs on a website, and they don't even bother to mention the X-max. Which implies that it is really embarrasing. They are way too cheap to be any good. It is not surprising that they burned out. The stamped baskets alone are the first indication that they aren't worth buying.
Boxes are cheap btw, so I wouldn't bias your choice to keeping the box you already have.