yep, step 1 is to desolder the controller and put a socket with teensy++ in its place, then map the matrix to your favorite keyboard layout. You will have to cut a few traces to "move" the power and ground lines to the right place on the new microcontroller. looks like pin 3 on the bottom right is either ground or power (you can tell by checking which side of the LED it goes to), so that will have to be moved. The other power trace looks like it goes to pin 40 (top left on the back)
I only recommended teensy++ as it has a lot of IO for that 40-pin chip that's there already. You can get by with a smaller IC like standard teensy, but you will need expanders to deal with all the columns. You'll know for sure what' will work once you get the matrix traced out.
Overall it's a great project but you will put more money into it that it will take to buy a new keyboard, so make sure you are very happy with the switches and build quality before you start! Otherwise it will be better to start with a different donor board.
Spacebar will likely take normal costar stabilizer inserts.
I dig the reversed bottom row!
schematic will pretty much be the pinout of your IC, put all the IO pins into the rows / columns and make sure the power is going to the right pin. up to you if you want to reuse the connector that's there, or just wire the usb end of the teensy out the case. But pretty much the kb matrix is the whole schematic. If you have bluetooth, it will communicate with your controller on a standard digital interface, perhaps SPI, so you would take some unused IO pins and wire those to the BT. Then in the firmware, you would just set those pins to communicate with the BT.
Good luck!