Perfectly aligning two complex surfaces

I have two complex surfaces; the smaller surface is a subset of the larger surface. I want to find the correct rotation/translation which causes the two surfaces to stack perfectly. I’ve done the very best I can by eye, but there is always some very small misalignment between the two surfaces.

Some context for this problem: way back when I began a site plan, I brought in location terrain data. The location terrain has since been rotated and translated (but never scaled). I now would like to bring in more terrain data (the same location, but a larger extent), and align the new terrain perfectly to the old one, so that all the elements of my site plan remain where they should be.

With Align Tool (Didier Bur) - JHS POWERBAR v2019