Another step you might want to add to your process is to first use Remove Silence on the reference track(s) to gate out any noise that can cause Audiosnap to mislocate transient markers. Otherwise, you can end up quantizing clip start times that don't accurately represent the actual drum hits.
I noticed a little of this going on in your video when you were zoomed in briefly. Look at the start of the highlighted clip at 7:07 in the video. The clip is quantized to 6:03:480, but the kick is a about 30 ticks late, whereas the next one at 6:04:480 looks good because the transient marker was right.