In the last 40+ years, I have never seen a .38/44 as an offering by any major ammunition company. They have normally been called "Hi Speed", "Hi Velocity" or something akin to that. I think there are some .38/44s that are head stamped as such, but they date back further.
The only real criteria we have for the load typified as a .38/44 is one that is advertised as producing about 1100 fps with a 158 gr bullet.
According to Phil Sharpe, page 409 of the "Complete Guide to Handloading", 6.0 gr of Unique, with a factory 158 gr lead bullet and a seating depth of .273", produces 1076 fps at 18.500 cup. If you increase that to 6.6 gr of Unique the velocity goes up to 1130 fps at 20,900 cup. The lower load is within the cup specs for .38 Special (18,900) and the heavier load is within cup specs for +P (22,400).
Other than that, I don't know of any place to get pressure data for anything resembling a .38/44 load.