Child seat: how to keep the child's head from falling forward?
Here is a solution that actually worked very well -- and during our testing it appears safe to use, seemingly also in the event of an accident. (If you disagree, please explain why!)

What we did was to loop a thick soft rubber band around the helmet's headband, and then secure the other end of the rubber band to the seatback using a bit of string through one of the shoulder-strap openings, to achieve a horizontal pull.

Earlier, we tried looping the rubber band through one of the helmet's air vents, but this caused problems: pulling the helmet back towards the neck revealing the forehead, and potentially putting upwards pressure on the chin strap. Evidently, the helmet's shell should be left alone.  

Attaching the rubber band to the helmet's headband was much better. As you can see from the photo, it provides a very level pull (not angled) in the perfectly opposite direction of the force of the falling head. The length of the rubber band also allows sufficient freedom of movement so it doesn't restrict the child when he's awake. Since the headband is already designed to spread the pressure evenly around the head, it also appeared to comfortably spread the "hold-back force" (feel free to edit my lacking English).