How does this apparent greater excursion range
at the beggining of the flight (If true for other flyers and not
something only present in the pigeons in my city) scales with size?
On average, with increasing body size, span, and speed - relative
flapping amplitude decreases. Pigeons use a very wide flapping arc
during steep, burst launches because of the launch angle and speed
regime (they are in an anaerobically powered, steep-climbing vortex
ring gait, and this requires a relatively large flapping amplitude).