I thought the reckless act (not the ensuring harm) still had to be deliberate: you knew (or should have known) something was overly risky and yet you did it anyway. Speeding as part of a drag race is reckless; speeding because the accelerator was stuck open is, I think, not.

In the trolley problem, you certainly can't be negligent (unless you own the trolley line or something). I'm not sure you could be called reckless either if your decision was meant to do the most good.