Very brave! I like this. I'm an experimenter also.
i all, iv modified a BT359 bluetooth gps. iv managed to cut it in half, work out the power and tx pins. and attached to a sd shield. Its all working fine, gives the correct lat and long, time, altitude and everything else that is should but the date only appears as 2000?
When you cut it in half, are you certain that the tx line voltage levels internally are capable of driving a 5v TTL input? Does the GPS have a solid ground connection to the Arduino?
Do you have access to an o-scope to check the input voltage to the Arduino? It may be just marginal by the looks of the output above.