steady.... Reckon your 3-3/4" .44 has a stainless Blackhawk grip frame, which is shorter than on the standard SBH.
Unsure what you mean by Super Blackhawk Bisley .45 ACP/.45 Colt Convertible.
The traditional Blackhawk Convertible is blue, with aluminum Blackhawk grip frame. Only stainless Convertibles I'm aware of are distributor exclusive and are called Bisley Blackhawks (and use same frame as SBH). By acquiring this model you would then have two steel grip frames.
However, the "ears" (radius) at the top of the respective grip frames require careful blending. Perhaps Flatgate or others who have made the swap will chime in. I have mated the factory Bisley to the Super Blackhawk, which requires no refinishing with stainless. I have not put a Blackhawk grip on a Bisley.
Ruger originally wanted to introduce the Bisley grip on the .357 Maximum in 1982. A few years later, when the Bisley grip was introduced, it was intended that the grips would interchange without any changes to the cylinder frame. Didn't work out that way. Radius of the hump below the recoil shield doesn't quite match, and that is where the custom blending comes in.
David Bradshaw