Spheroid line_interpolate - but in the other direction

Question

Using boost::geometry::line_interpolate with boost::geometry::srs::spheroid, I'm calculating great circle navigation points along the shortest distance between 2 geographic points. The code below calculates the navigation points for the shortest distance around the great circle. In some rare cases, I need to generate the longer distance that wraps around the globe in the wrong direction. For example, when interpolating between a lon/lat of (20, 20) to (30, 20), there only 10 degrees of difference in the shorter direction and 350 degrees in the other. In some cases I would like the ability to want to interpolate in the longer direction (e.g. 350 deg).

This 2d map shows shows the 10 degree longitude difference in red, and 350 degrees green. I drew the green line by hand to the line is only an approximation. How can I get the points for this green line?

This code is based on the example from boost.org, line_interpolate_4_with_strategy

#include <iostream>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>

int main()
{
    typedef boost::geometry::model::d2::point_xy<double, boost::geometry::cs::geographic<boost::geometry::degree> > Point_Type;
    using Segment_Type = boost::geometry::model::segment<Point_Type>;
    using Multipoint_Type = boost::geometry::model::multi_point<Point_Type>;
   

    boost::geometry::srs::spheroid<double> spheroid(6378137.0, 6356752.3142451793);
    boost::geometry::strategy::line_interpolate::geographic<boost::geometry::strategy::vincenty> str(spheroid);

    
    Segment_Type const start_end_points { {20, 20}, {30, 20} }; // lon/lat, interpolate between these two points
    double distance { 50000 }; // plot a point ever 50km
    Multipoint_Type mp;
    boost::geometry::line_interpolate(start_end_points, distance, mp, str);
    std::cout << "on segment : " << wkt(mp) << "\n";

    return 0;
}