"I'm looking for 38/44 Heavy Duty (aka 38 Super Police)"

Not the same. The .38 Special Super Police cartridge is simply the standard .38 Special with a 200 grain lead round nose bullet. The .38-44 (not .38/44, not Heavy Duty) cartridge is a heavily loaded .38 Special normally with a 150 or 158 grain metal capped bullet. Boxes usually say something like .38 Special Hi-Speed (Remington), Super Speed (Winchester) or Super-X (Western). There are numerous antique ammo dealers, and it is not that difficult to find a full box. It was loaded until the early 1970s. I have seen several boxes recently at gun shows. Try IAA.