A leap-month birth near a two-hour time boundary creates two separate uncertainties. Preserve the original record before changing either one: calendar date, leap-month label, local clock time, and birthplace. If the time was only approximate, record a range.
Hold the birth hour fixed while comparing leap-month rules. Then hold the calendar rule fixed while comparing times on either side of the boundary, including any true-solar-time correction. Save each candidate chart. Life events can help ask better questions, but they do not prove a calculation rule. Keep the software setting and school visible whenever you compare interpretations.