First, for the reason NikA wrote, if you pride yourself on accuracy, it is a horrid idea. Bouncing and skidding your bullets off the sides of a long chamber then the throat is the opposite of what you'd do to achieve the accuracy required to be competitive in NRA Conventional Pistol (bullseye) or silhouette matches. Also, the rear ends of your .38 Special and .357 Magnum brass would swell about 0.012" more than normal.
You did not write if your new cylinder has 6 chambers or 8. Either way, their is the question of who, if anyone, makes moon clips that would fit a Redhawk and the cost of those clips. Without clips, expect no extraction and either no ignition or missfires. It is possible the 9 mm Luger cartridges might head space on the taper but good luck with that.
My negative opinion aside, a few well respected members of the best known forum for that other brand (hint: S. W. .com) proudly brag their reamed S&W .357 cylinders shoot .38 S&W, .38 Special, .357, and in moon clips .380 ACP, 9 mm Luger, .38 ACP/Super, 9 mm Winchester Magnum and a few lesser known 9 mm cartridges. While they are pleased with the accuracy they get firing 9mm Luger I've never seen them write specific group sizes or distances. If you try it please report specifics of the accuracy that you get. I've been wrong before.
By the way, Redhawk and Super Redhawk .44 Magnum cylinders have the same part number and .357 versions of the Super Redhawk exist. If my memory is good they are, or were, sold as Super GP 100s. Consequently, installing a second reamed .357 cylinder in a misnamed Super Redhawk is possible.