The elliptical transfer orbits treated in the preceding posts are what I've come to call "elliptical transfer orbits of the short path," meaning that the transit object moves through an arc of true anomaly less than pi radians.
For each elliptical transfer orbit of the short path, there exists an elliptical orbit of the long path, in which the transit object moves along the same orbit in the opposite direction.
Long path elliptical orbits differ from short path elliptical orbits in the following ways.
At each point where the HEC position vectors are identical, the HEC velocity vectors differ (only) in sign.
The sum of the transit times for the long and short paths is equal to the period of the transfer orbit.
The inclinations sum to pi radians.
The angular momentum vector of the long path orbit is the reverse of that of the short path.
The longitude of the ascending node on the long path will be that of the short path plus or minus pi radians, whichever will keep it inside the interval [0 , 2 pi).
The sum of the short-path and long-path arguments of the perihelion should add up to pi radians +/- some whole multiple of 2 pi radians.
The sum of the non-apsidal endpoint true anomalies for the short path elliptical orbit and for the long-path elliptical orbit is 2 pi.
And the like.
There is yet another class of intercept orbit, which might be called a super-periodic transfer orbit. They may be either prograde or retrograde, as we normally reckon such, and involve transit times exceeding the transfer orbit's period.
Such extra possible orbits gives a spaceship pilot more opportunities to find a valid transfer orbit, however at the cost of increasing his transit time, often greatly.