After looking at the video, I feel you could have a second problem. Yes, it is possible that the steppers are running too fast, but it is also likely that the drive screw is binding with the drive nut. It is interesting that it binds mostly in the direction of easiest motion, down (The motor is being assisted by the weight of the carriage assembly). This can come from misalignment if either the screw and/or the nut. Make absolutely sure that there is no binding. Turn off the power and turn the screw by hand and make sure that it turns freely the entire length of the screw, especially near the limits of travel.
If the screw is out of alignment, it will bind, or Get noticeably harder to turn, near the limits of travel. You may want to take some of the weight off the carriage to make it easier to feel.
If the nut is binding, it may happen near the screw center where shaft whipping can come into play. To test the nut for alignment (it may bind anywhere on the screw), loosen the nut, in its mount) so that it can freely follow the screw, and run your up/down test. You may notice that the jamming has stopped. If this is the case, you will need to make sure it stays aligned when you tighten it down again.
It is surprising how critical these adjustments are for smooth operation. I would first Align the screw at both ends several times to make sure it runs true with the nut, then make sure the nut is straight. Then do it one more time. The Z axis us usually more forgiving than X and Y.
If the unit has been in service a long time, the nut can be filled with debris (especially cutting plastic). If this is the case, the screw will be hard to turn anywhere on the shaft. Cleaning the nut threads will fix it.
Thanks.
Bill