I think it is likely an alignment issue also because my bike was doing the exact same thing - leaning and pulling hard to the left. I noticed that sighting straight down at the front wheel, I was seeing the left side of the entire wheel. I looked at the way I was seated but that was not it. I finally turned the bike over and stretched a string from the front to back wheel. and found an offset of 3-4 mm. I also leveled the bike with shims under the bar, using a 16" (43mm) carpenters level and found the wheels were not plumb. After considerable pondering over many weeks, and with some hesitancy, I filed the front front dropout a bit, and then rode the bike for a while. Stability seemed improved some so I filed a bit more. This went on for several months, evaluating stability after each session of surgery.
The bike now can be ridden no hands but even better, holding a line in a corner is a pleasure as is diving into fast switchback turns. The improved stability feels good on fast descents.
I've since calculated that an error of 1/2 mm in placing a dropout produces an error at the rim of 3-4 mm. I hope this helps you track down the problem.