As far as I know, there's no recompose tool by that name in Photoshop. There
is a Content Aware Move tool that also has an Extend function, but I tried a different route that involved the Rectangular Marquee tool and transformations. First, I selected a rectangle that included the whole image on the right side of the dogwood and compressed it horizontally to the left with Edit>Transform. Then, I used the Crop tool to get rid of the now empty region on the right and extend the canvas on the left. A rectangular selection from the left edge of the image to the dogwood and an extension transformation of the left edge effectively moved the dogwood to a Divine Proportion position. (Actually, I had to finesse that with another application of the Crop tool with the Golden Ratio overlay.)
When I went back to Photoshop to work on an image, this was still up, and I noticed a vertical line just to the right of the dogwood where the left edge of the selection would've been. I'm sorry I didn't catch that, earlier, but it's an easy fix with the Spot Healing Brush tool.