Excellent. Thanks for the details. I'm trying to figure out a child passenger option without going full cargo, so this is worth a ponder.
Yes, I appreciate this as well! We have a cargo bike now, but I've often thought that going with a stronger rear seat would be a cheaper and still satisfactory option. The bobike junior (http://www.bobike.com/en_en/bobike-junior-classic.html) seems pretty good, but I think it's also over $200. My 5 year old enjoys the trail-a-bike, too. We found one in decent shape for $5 at a yard sale and I commonly see them listed under $75 on kijiji and craigslist.
Did you get a special rear rack? My hybrid bike has disc brakes and the rack isn't terribly sturdy because it has a multi-jointed support arm to go around the brake; I wouldn't trust it with my 50 lb son. I seem to recall seeing some stronger racks that mount on the wheel's axel. That, combined with your idea to use a stem on the seat post, could give a beefier, more versatile and cheaper system than the bobike junior.
I rigged up a child seat on my bike similar to what's being described here, and used it from when she was 5 to 7 years old (at which point she had enough stamina to ride her own bike for our errands). She's always been a big for her age kid, in the 95 percentile, so more like an average 6 to 8 yr old. She was probably 60-70lb when we stopped using it.
I had a sturdy rack onto which I strapped an actual bike seat we had spare in the garage, cutting a curved notch in the stem post where it met the rack (think like the way log cabins slot together) and securing it all with various zip ties and a jubilee clip. Then I added a set of tandem stoker style handlebars to my seat post - functionally the same as the broom handle above, but were actual small shaped handlebars with proper grips, giving her a natural riding position. Finally, I strapped foot pegs on to the... um... narrow, horizontal bit of the frame that goes to the rear wheel hub, dunno what that bit's called. I had panniers too, as a safety skirt, as I often dropped her at school then went shopping. She could actually put her legs over the top of the bags if necessary, like a small child riding a very fat pony :)
It all worked brilliantly, and I regularly got stopped for people to admire it, and examine how it all went together so they could do something similar.