is it possible that setting a lower airspeed makes a steeper climb?
I think you have it backwards, it is not that a slower airspeed produces a steeper climb, it it that a steeper climb, given the same power, will cause a slower airspeed.
If the only constraint you're setting the FMS is the airspeed to maintain for a constant thrust, then it will pitch up more, increasing the rate of climb, which will slow the airspeed.