Here is a simulation of the Jaakko Tähti 44° parhelion display. In order to produce 44° parhelion (left arrow) in the simulation, multiple scattering has been used for plate crystal population. Reflected Lowitz arcs (right arrow) as well as 22° halo are simulated with "normal" single scattering populations.
Photo and simulations are also found here. Simulation is made with program by Mika Sillanpää and Jarmo Moilanen.
Patrik Trncak notified me about another likely case of photographed 44° parhelion. It was documented by Matthew Hyde in Greenland in summer 2002.