"but the Action did not record my dragging the origin to the lower left corner." The drag or using the arrow keys when the move tool is selected puts Photoshop into a "follow on" or "reusable" action. Instead of recording "move one pixel down" over and over and over again Photoshop keeps track and just ends up with "move 4 pixels down." If you have actions panel recording you can see this, select move tool, move with arrow or mouse, then do something else, like select another layer, and you get two entries in actions panel, the final resting spot of the move and the layer select. If you can get the dimensions and location of the thing you are moving then just move it to "0, x" for left, "x, 0" for top. Does that work?
But I DO like the idea of a command that says, "move to the top" have you played with the alignment options in the move tool bar. Select two layers and pick: "Align vertical centers" that records in the actions panel.