Instead of a dropdown list, you could use a popover with a scrolling portal. This would allow you to control the size of the list.
Popover is worth trying out. To answer the question about direction, my quick checking indicates:
1. drop down lists will always drop DOWN by default unless there is insufficient screen space below the object, in which case it will drop UP, and the size of the list box will remain the same.
2. popup menus will also drop down by default, and will continue to do so much closer to the bottom of the screen, the size of the menu box reducing accordingly.
Thank you for the info. I will try the popover.