Mike, I just got back from looking at the ceramicssf site. Yup, 18 x 18 x 1. It's disappointing that they don't sell a 17 x 17 x 1 stone. If you cut off an inch, will a 17 x 18 x 1 stone fit in your oven? If you're willing to do that, then that will give you the 4 minute bake.
1/4" steel plate, huh? You just love cutting it close, don't you?
1/4" steel at 620 f... 1/4" steel at 620 f... I don't know, maybe. On the positive side, 1/4" x 17" x 17" will probably run you as little as $20, so you might as well try it. I know I said that the heat from the bottom element can't reach the pizza with pizza stones, but 1/4" steel could very well be one of those very few exceptions to that rule. Another plus is that your pre-heats will be quick- most likely less than a half hour.
Think about 1/4" steel or 1" cordierite-mullite, and, if you get a chance, try timing one of Avellino's bakes.
And, in the meantime, do the 61% hydration/1% oil version you are planning. Also, you might want to think about a 2% oil version. Anything up to 3%, imo, is within the NY style parameter.