@ChrisM I see you put up a nicely detailed post on Cargo Bike Republic yesterday and already have more responses there there than you have here after a week or two. No substitute for going to where the right eyeballs are doing the reading.
I never would have looked at or even knew about what seems to be the quasi-consensus bike being suggested: The Bike Friday Haul-a-Day and Ever-E-Day. The two of them are light weight, and the latter bike, before you get to the motor part, weighs less than 27 pounds! So we all learned something here. Plus its smaller wheels mean lower center of gravity which is a big deal with a child on the back.
You are still making compromises here, but those compromises give you everything you asked for (except for the price point). The Haul A Day is a stronger choice but its a bit heavier and larger. And of course more expensive. It has a center stand which is a big deal for safety and convenience with the child. You really want a center stand to keep the bike stable while you pack the little one on or off, or want to step away from the bike for a moment.
The Ever-E-Day's rack is pretty clever in how it slides into the chainstays. That and its overall construction solves for sturdiness.
The kickstand on the Every E Day sucks, but you should be able to find a bolt-in replacement center stand (something from Ursus maybe) that will address that.
It looks like they are using the Tongsheng TSDZ2 mid drive which I am not crazy about, but its a better fit to their frame than a BBS02 would be.
@PedalUma is the Tongsheng guru around here.
I don't know if you've found what you are looking for, but at least you are getting good additional, experience-based perspectives. Bike Friday wants $1100 for adding the motor and battery (only $880 for the Haul A Day so thats worth mulling over) which I can pretty much guarantee you can beat by a mile with some help and advice... but you then have to do the install work yourself.