I'm gonna be an a$$ here and first tell you that it is a Power INVERTER you are using......not a CONVERTER. Coverters convert AC power (usually 120 Volts) to DC power.....Inverters do the opposite.
sorry.......I am an electrical engineer
Okay, this is going to be a long-drawn out explanation so I apologize.
That said, just be careful that those powered subs don't over-work your power inverter. You can buy inverters of various power capabilities, so just like when you install a new car amp/subs, you have to check the peak ratings of your equipment against what your electrical system can handle. If the inverter can only produce 300 watts of AC power but your powered subs demand 350 combined, you'll blow the fuse in the inverter.
Also, if your battery and alternator can't produce that 300 or 350 watts anyway, you are wasting your time. Power inverters aren't a magical device. They, like all other electronic devices, can only output as much power or energy as they have available for use. That 300 watts still comes from the car's electrical system. Also keep in mind that you lose A LOT of power just in the inverting process (you have noticed that the thing gets warm I'm sure) and even more in the coverting process (the AC power adapter that runs the subs).
I would suggest keeping your MTX subs and getting a better box. That is the only reason the home theatre sub sounds better.....its ported correctly. Get a properly ported or properly sized sealed enclosure and I think you will have better results....and won't wear as heavily on the vehicles electrical system. JUST A SUGGESTION. Otherwise, theoretically.......just get an appropriate wattage power inverter with 2 taps. Don't be shocked if your performance degrades significantly (no promises)
Be careful...be safe!!