If your bridge is the same as the images you linked to, then you will have a separate tailpiece. The bridge does not have to deal with string tension, just the downward pressure. If this is so then the metal bridge could be replaced with a similar sized piece of ebony or rosewood. A slot could be routed in that to take a saddle, an undersaddle acoustic pickup might be fitted under that and connected to a standard acoustic guitar preamp. You would loose the tuneamatic bit and have to rely on standard acoustic saddle compensation. No big deal.

The undersaddle pickups/preamp deals from China were very reasonable last time I looked. If you don't want to hack the guitar about to mount the pre amp you could look at a belt mount for it.