Your choice, I have both types in use. Whichever material you have to hand or find easier to work with.

Won't the CI backplate be kinder to the spindle?

Nodular cast-iron is three times stronger than ordinary cast-iron, which is good when centrifugal forces are applied by a high-speed lathe. Chucks are sometimes marked with a max speed rating.

Steel is stronger than cast-iron of any type, so a backplate made of it is safer. In theory a cast-iron backplate would damp vibration better, but I doubt the difference is detectable, especially at lowish rpm. So I agree with Jeff and wouldn't go out of my way to get a cast-iron backplate blank if I already had some suitable steel to hand.

Interesting machine – nothing to do with the question, but can you share some photos?

Dave

If I had a choice, I would always make backplates out of nodular (SG) cast iron. Why, it is easy to machine and doesn't make the mess of dust that ordinary cast iron does. The common blanks available, however, are the messy type, and having a magnet close to the tool tip can catch some of the dust. Steel is perfectly acceptable if your tooling works well with it. Having to make the register and thread without a gauge can be overcome quite easily. If the blank backplate has been faced off flat on the side which the new chuck will mount, and then turned round and clamped to a faceplate, the register can be bored to about 0.001" larger than the spindle register. The thread if Whitworth form will be 0.064" deep, so the starting bore will be 1.247" The thread if UNC form will be 0.065" deep, so the starting bore will be 1.245"

Just touching the threading tool in the bore and then cutting to a finish depth of 0.064", or 0.065" will give you the nominal size. Adding an extra 0.002" on a thread this coarse will not do any harm whatsoever. To check the fit on your spindle, just unscrew the faceplate with the backplate still clamped on and try it out. Should it prove to be too tight, just remount the faceplate, and with such a coarse thread, you can visually check the alignment of the tool in the thread in case it requires a slight adjustment.