Is the hole at the bottom front of the water pump dry or wet? Water pump seal might do this. If you have actually seen the water squirt out otherwise forget this.

I might even take the belt off and check for wear in the water pumps bearing. Really sloppy and it is time for a new water pump anyways. At that many miles the water pump if original is probably somewhere near the expected end point of lasting. If everything seems dry. You might have to pressure up the coolant system to find the leak.