TUE,
Normally, a backplate is machined backside first, then mounted directly on the lathe spindle to face the chuck mounting surface; but in this case it sounds as if you are making it for a milling attachment that doesn't have the same thread or register, is this correct?
If you need to make it to fit something with a different size spindle than your lathe, I would turn and thread a stub to match the spindle it needs to fit and, without removing the stub from the lathe, thread the backing plate on this stub and face it off. If you still have runout problems after doing this, I would check the spindle on your indexer for runout or damage.
Kevin