Ah! Sounds like you're ahead of me in parenthood experience. (I've one boy, one girl.)
There's a lot to be said for designing your own layout. I did something similar to your approach before settling on Oran: I took a left hand only Dvorak layout designed for regular keyboards and tried to reimagine it for the Twiddler. After that, it's just a case of looking up frequent bigrams and seeing what's easy to put in.
I also tried one based on Qwerty for a blind friend of mine: he wanted to have the twelve buttons mapped as follows:
q w e r
a s d f
z x c v
then we had the concept of a mirror button to get the other half of the keyboard
u i o p
j k l ;
m , . /
Think we reversed the order. At that point muscle memory greatly reduced the learning curve, but the disadvantage was some of the combos became quite unwieldy. Mind you, you could now use a thumb button for mirroring and it's possible to use multiple buttons in the same row to hit bigrams: it could be worth revisiting if you're looking for an approach.
Bigrams (or more specifically multi keystroke chords) aren't working on the T4 at present. I've had a support request open since last Friday on it. Hopefully they'll have this fixed in the time it takes you to learn the individual character typing, so no need to wait.
I'm afraid my PowerShell layout printer only works for the old chord notation. I'm unlikely to have a chance to look at it for the next month or so but I'll post here if I get it working.