Minimum acceptable self-launch climb rate

I really would like to second Steve message.
Because the prop used on existing self launchers have very little speed Range, their pitch is selected to provide a narrow compromise between takeoff speed and climb speed.
This allows to have sufficient thrust during takeoff run, but reduces the climb speed.
From my precedent message, it is not pleasant at all, especially when density altitude gets high and the feeling gets worse with low IAS and less than 3 knots of climb.

Modern props with significant ESR effect (Extended Speed Range) could be used to improve the situation without compromising performance (you would still get the higher drag from the pylon/engine).

When looking at the GP prop, they seem to be using modern airfoils which should exhibit the necessary ESR effect (good question to ask GP)
Because of the low drag pylon and better electric motor speed/torque control, the climb rate should be good over a large speed range compared to existing combustion engine self launchers.