Once done with the cook, I OPEN the vents 100% and allow the coals to completely ash out. The next morning, I transfer the ash, by hand (messy but insurance for sure!) into a plastic grocery bag, and then in turn to a galvanized trash can. I discovered LONG ago that throttling down and trying to snuff coals like you mention, just doesn't work. Yes I have had a flare up in a trash can because I didn't let them burn down to ash...
Often I grill with sport sandals. Been doing so for decades with no issues.
Chimney goes on the ground, a good way away from the grill, people, or anything flamable.