Not with the 44 caliber, but I have shot a bunch of the Lyman #358101, a 75 grain WC for 38/357 revolvers. A 36 caliber RB (375") for the Colt 1851 cap & ball revolver weighed about as much as these #358101s do, and the 150 grain 44 caliber WC you mention is close in weight to the 140 grain RBs used in the Colt 44 caliber (.451") cap & ball revolvers. In short, these two wadcutters seem analogous to one another between the calibers.
One bullet seated flush shoots low at 25 yards with a load of 3.0 grains of WW-231, but form a half-decent group. 2 bullets seated atop one another in the case shoot close to where the sights are looking, and hit close to one another at 25 yards. (Same 3.0 x WW-231). I pranked one of our PPC mavens with 6 of these rounds in his Davis wadcutter gun; all 12 hit inside the 10-ring, and only 3 hit outside the X-ring of the B-27 (25 yards). It took a minute for the guy to figure out that He Had Been Put Together. He enjoyed the joke, and once told of the "doubled-up" WC bullets he was pretty impressed with how well the squatty little bullets shot. "You are an evil jerk, Allen!" was his conclusion. Perhaps so.
I have also sized down .375" and .440" RBs to .358" and .431" in my Lyman H&I dies--seated them into 38 and 44 cases with 3.0 (38) and 4.0 (44) grain weights of WW-231 just for grins. These also shot low to the sights, so for target purposes some adjustment for barrel time or recoil roll-up will need to be made. They grouped OK, and if the sights and impact could get on the same sheet of music these loads could have utility for small game and varmint applications. I haven't pursued the question in great depth or breadth, but I have done this much--and perhaps it answers a few preliminary questions about the practice.