But you know that'll fail?
Yes. I believed I was eventually going to have to inject additional 1s into the 11-stepper to generate enough single-digit factors to get at least 233 digits in the 12-stepper. And I knew the chances were that the first 11-stepper, even with 1s, might not ever be able to generate a 12-stepper. Since the conjecture is that there are no 12-steppers -- though there isn't a solid mathematical reason, other than "233 digits wasn't enough for 12-step, when 15 digits was sufficient for 11-step, so it's not likely to have any 12-steppers" -- the chances are small than any amateur (like us me) will find a 12-stepper. (Though mathematics does have some strange outliers, like the Monster Group being so far out there, or the sixth platonic-solid-analog in 4d, when all other dimensions have fewer.)
update: I am an amateur at mathematics. I should not have spoken for anyone else. Sorry, LanX.