Water Pump, Head-gasket, Engine?

I nearly blow a head gasket every morning in the first 10 minutes. Oil - good, coolant - good, life - eh. Engine temp seems to rise to 227+ when going up a little hill on the 101 in LA. I hear the water pump rpms may not work at a certain point. This is caused by a faulty water pump having a crack/break in the coating in spindle inside of it. Seems it’s a place to start as I have made sure there are no air bubbles in the coolant by bleeding it a couple times at the highest point, where the coolant hose goes into the top of the EGR. Any experience with this? I’ve read the other forums and have not seemed to find an exact cause so I can do some maintenance repairs.

I prefer not to drop an engine in the car for $2k, even though it is a low mileage Gen 4 motor.

My car: 2013 persona with 234,500 miles.

 

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It has not been changed yet. Looks like I’ll be doing it within the next week.

 

Unfortunately the hybrid assist app does not show that. I read up about people using scan tool to get that info but nope, I personally don’t have a way of snagging that.