The "square" plate is different for White than for National, but so far all the National Rotary machines I've seen have the same attachment type.
I've since figured out that New Home also fits Singer. I was just trying to install it wrong, and could not get it to fit. You need to tip it completely vertical, and then the tab fits into the hole, and then you lay it down and install the bed screw to hold it in place. That tab won't go in unless you have it tipped all the way up.