Seems you could, instead of using the numerology thing, use the Major system of memorizing numbers. So “dog” would be 17, hence mod9 8, so thrown out. “hammer” would be 34, so mod9 7, hence thrown out. Umm . . . frog? 847, so mod9 . . . 1! Got a number!
Benefit of this approach would be that you’d have the Major system (which I’ve been using since I was 16 (or, you know, “dish”) years old) for free, and not have to do a lot of addition in your head. I doubt it’d be nearly as random, though. Still, the Major system is hella useful.