I agree, your horse is falling onto the forehand.
To do the transition from canter to the trot, I squeeze with my thighs, which is a general downward cue. My legs support active steps and balance. I don’t rely on my weight or really sitting deep in my seat, because those (to us) are cues for collection, and I want the horse to eventually collect with those cues. Sure, one should collect a bit before the downward to trot, but I don’t want my horse to trot off of my weight changes. I use my thighs to ask for the canter-trot and I stop following the canter with my body. Canter walk - I collect and think about a bird alighting on a branch from flight. Collect collect and then use my thighs to say walk. For me, this teaches a clear aid.