ColdWaterSandwich
Member
The Rinnai is fixed!! 
It was the bypass flow control valve. The tech reviewed all the testing with Rinnai and they agreed it was likely the flow valve, shipped him one, he swapped it in, and it's working great now:
-Output temp comes up to seet temp way faster
-HEX output temp stays much closer to heater output temp (typically ~150sF for 125F output temp
-No longer drops temp dramatically when a vanity faucet is turned on while showering
-No more flame cutoff when the vanity then is turned off
-Overall dramatically more stable output temps.
I kept the old valve and disassembled it last night. It was totally stuck. I first took out the screws that hold on the electric motor, exposing the gear that rotates the valve in the housing. Could not spin it with my fingers at all. Pulled the valve part out of the brass housing so that I could have good leverage, holding the outer plastic part while trying to spin the actual valve part. With the leverage I now had I was able to force it to turn, back and forth, and after a few full rotations I was able to spin it open and close pretty freely. The valve would probably work fine now, at least for a little while. No idea why it failed in the first place, but it was absolutely stuck in the open position, with little if any actual motion based on whatever input signal the motor was getting
The tech did ask Rinnai about the lack of error messages, and apparently this isn't unusual in this situation; the HEX was definitely getting hotter than usual but not enough to trip the error code, and because the output of the heater was (eventually) close enough to set point (though unstable when flow changed), it didn't make any other codes. The flame going out when flow drops a bit was due to incorrect understanding by the brain of how much flow there actually was; it thought more water was going through the HEX than actually was.
It's unclear how much this will cost me; the parts are under warranty but probably not the labor. There's one more part backordered that he is going to do on a precautionary basis due to a buildup of crust around the pressure relief valve (inside the heater); there is a tiny leak. After that, he will submit paperwork and find out what is actually covered.
I did a bunch of tests today; so far so good. Thanks for all the input, ideas, and support.
I will update again once the other part is replaced and I get the bill.

It was the bypass flow control valve. The tech reviewed all the testing with Rinnai and they agreed it was likely the flow valve, shipped him one, he swapped it in, and it's working great now:
-Output temp comes up to seet temp way faster
-HEX output temp stays much closer to heater output temp (typically ~150sF for 125F output temp
-No longer drops temp dramatically when a vanity faucet is turned on while showering
-No more flame cutoff when the vanity then is turned off
-Overall dramatically more stable output temps.
I kept the old valve and disassembled it last night. It was totally stuck. I first took out the screws that hold on the electric motor, exposing the gear that rotates the valve in the housing. Could not spin it with my fingers at all. Pulled the valve part out of the brass housing so that I could have good leverage, holding the outer plastic part while trying to spin the actual valve part. With the leverage I now had I was able to force it to turn, back and forth, and after a few full rotations I was able to spin it open and close pretty freely. The valve would probably work fine now, at least for a little while. No idea why it failed in the first place, but it was absolutely stuck in the open position, with little if any actual motion based on whatever input signal the motor was getting
The tech did ask Rinnai about the lack of error messages, and apparently this isn't unusual in this situation; the HEX was definitely getting hotter than usual but not enough to trip the error code, and because the output of the heater was (eventually) close enough to set point (though unstable when flow changed), it didn't make any other codes. The flame going out when flow drops a bit was due to incorrect understanding by the brain of how much flow there actually was; it thought more water was going through the HEX than actually was.
It's unclear how much this will cost me; the parts are under warranty but probably not the labor. There's one more part backordered that he is going to do on a precautionary basis due to a buildup of crust around the pressure relief valve (inside the heater); there is a tiny leak. After that, he will submit paperwork and find out what is actually covered.
I did a bunch of tests today; so far so good. Thanks for all the input, ideas, and support.
I will update again once the other part is replaced and I get the bill.