last week a judo black belt showed me some tips with tai otoshi. he showed me how the lower body sets up a supporting structure, while the real throw comes from a trunk rotation. in exercise terms, it's more like an olbique russian twist than a wood chopping motion/ball slam motion. the rotation occurs in a very, very thoracic region after the lower body has been set up.
now i understand why harai goshi and tai otoshi are completely different. it's like day and night now.