All of those methods work, as does the Move tool. With the Move tool active and nothing selected in the model, hover the mouse over an unconstrained end-point of the edge. Click-and-release the mouse, and start moving the end-point in the desired direction. You can click-and-release a second time to determine the new location of the end-point, or you can type a dimension and press Enter (in which case the end-point’s new location will be in the direction of movement, with the specified distance from its initial location).
Adding an additional edge to extend an existing edge works OK visually, but personally I wouldn’t like the resulting geometry that contains two co-linear edges. I haven’t tried this, but perhaps one way to cause SketchUp to merge the two short edges into one long edge may be to draw a third edge at the intersection of the two short edges, which heads off to the side (arbitrary direction, arbitrary length). Then delete that off-to-the-side edge. The deletion may trigger SketchUp to merge the two remaining co-linear edges.