Certainly it looks like a nice inverter and 'Ripping it apart is certainly one way of opening the device... But did you ever consider that the transformer might not be big enough to handle bigger Mosfets?.. Transformers stink when they burn..
This is from the sellers Ebay page...
Input / Output
Input: DV 12V / 500mA
Output: AC 100V - 240V
Max Output Power: 5W NOTE: Not for large electronics like Laptop computers, DVD players, Printers, etc <----- My emphasis
There are two things you have to consider when asking a transformer to do more.
One is the current rating of the wire, too much current and it will get hot.
However the second thing is the magnetic saturation of the core, that can limit what you get out of a transformer.
On the one hand, there's the raring to tear into this thing this way and on the other there's a reluctance to cobble up a little circuit from two or three components to find out what's going on.