Pull off the panel near the fridge that allows you front access to the heater. On the lower left corner of the water heater you'll see a valve. Shut it all the way, open it all the way and settle somewhere in the middle. It's only a half turn or so.
That cured it all, every symptom you have, for us. Water wasn't being held in the heater long enough to stabilize heat. We now use only the hot water shower valve, no cold water. Not a single hiccup since we adjusted that adjustable valve.
It's a 30 second fix.