Without any videos, it's kind of hard to tell, but based off what you described your motion to be, I don't think it's necessarily an issue about being too vertical in the pull rather than not pulling under the bar.
You mentioned that you "drop under." The pull under helps keep you connected to the bar, which aids in the proper bar placement in the rack position. In my opinion, it's ideal that you're going vertical. Sometimes, when a lifter has an arch, the bar tends to bump away from them, often exaggerating the very problem you described as having. Remember, we want the bar to accelerate upwards, not forward.
If your pull is good (good positioning, explosive knee AND hip drive with the thigh brush, tall extension), then I think you will benefit from third pull drills such as scarecrow cleans, tall cleans, dip cleans, and hang/block cleans. The same can be done with snatches.
Hope this helps,
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.