I might suggest you make your coordinate transform to UTM then make your distance calculations or next transform. The Geo::Coordinates::UTM module is bidirectional and supports many different Ellipsoids for the Lat/Long. I suggest using the WGS84 ellipsoid since that is the standard for GPS. The precision of these calculations is to the centimeter if not better, assuming that the earth is not a pulsating ellipsoid, which it really is. The one drawback is that the UTM system divides the planet into zones. Calculations across zone bounderys may not be as precise.

We (Center for Coastal and Ocean Mapping) do a lot of this, but in the metric system. We need that flat model to do measurement calculations.