In Second Temple times, the beginning of each lunar month was decided on the basis of two eyewitnesses testifying to have seen the new lunar crescent at sunset. Patriarch Gamaliel II (c. 100) asked the witnesses to select the appearance of the Moon from a collection of drawings that depicted the crescent in a variety of orientations, only a few of which could be valid in any given month. According to tradition, these observations were compared against calculations made by the supreme Jewish court, the Sanhedrin. Whether or not an embolismic month was to be inserted depended on the calculated estimate of the spring equinox moment, the condition of roads used by families to come to Jerusalem for Passover, adequate numbers of lambs to be sacrificed at the Temple, and on the ripeness of the barley that was needed for the first fruits ceremony....
The modern Hebrew calendar cannot be used to calculate Biblical dates because new moon dates may be in error days, and months may be in error months.
...so there is no way to bring a computer program to bear on the problem of determining what eyewitnesses were seeing 20 centuries ago, and thus determining exact dates from then. Sorry. What you need is the services of a professional historian, not a software developer.