Ended up talking through this with someone at Leica. I have fixed the issue but not the traverse. The following recap is for my memory or in case anyone else stumbles upon this. It may not be the best solution, but it worked.
1. Delete all "known coordinates"
2. Create a new text file with my starting 2 points (known, surveyed in).
3. Import the text file as my "known coordinates"
4. Run through the incredibly confusing and ass-backwards traverse editor to establish new coordinates on all of the occupied points, starting with the 2 surveyed points.
5. Print out the traverse report and key in these new coordinate values into a new "known coordinates" text file, appending on to the 2 survey points I started with.
6. Import in the "KNOWN COORDINATES" text file.
7. Create a registration and add the above text file along with all scan worlds. Auto-add constraints. All SW's have 3 constraints: BS, FS, instrument point.
8. One SW was just a spur point and hence had only 2 constraints. For this one I had to create a vertex common to another scan. This instance it was center of pipe column at top of footing.
Perhaps having a newer version of Cyclone would have helped and/or being more fluent with cloud registration. All in, it probably would have been quicker to have the crew re-do the project vs. the amount of time spent in office mucking with it. I guess I know for next time...