I don't have any experience with inverters, but I have a couple suggestions.
You may want to attempt to underclock your processor to see if you can get it to squeeze by. Changing the FSB to 100 is a good place to start, and you can subsequently lower the CPU voltage. The min voltage for your board is probably about 1.375.
A weaker graphics card will help out a lot as well. If you don't have one and feel this is worth spending time on, you can underclock your graphics card as well. That will involve saving the video BIOS, modifying it, and then reflashing the card.
I honestly don't think just changing the motherboard is going to improve your power usage dramatically. You should see the greatest difference by underclocking your processor. What processor are you using anyway?