Sorry I'm late to this, I had read it on my tablet and it was too hard to respond there. I may have missed it somewhere, but I really think the solution is far simpler than where these posts have headed.
I really think that trying to work to increase pressure/flow at the input is barking up the wrong tree. From the OP: "probably as it senses low inlet pressure." - The heater sense flow, not pressure. There was a chart in post #62 that showed the turn on/turn off points to be at 2.3 and 1.8 L/min. So once you are drawing hot water, you need to keep the flow above 1.8L/min, or the heater will shut back off. As the OP mentioned the problem is worse in warm weather, this makes sense, the user adjusts the faucet for a hot shower, but that takes less draw from the hot side in the mix, since the cold side is warmer in warm weather. This was touched on in post #5, but seems to have gotten lost.
The simple solution is to run a separate hot water faucet as you shower, to bring the total flow of hot water higher than 1.8L/min. Somewhat wasteful yes, but that's the simple solution.
My shower is ~ 4L/min total flow. OP should measure theirs. This was asked in post #37, but was rebuffed by OP. I guess maybe they don't want help?
I think another, more complex and costly solution was mentioned, to add a small-ish tank heater at the output, to buffer the on-demand heater. But that will also go cold eventually w/o enough flow to trigger the demand heater on.