Since it seems like we might be getting serious about using Hugin for the "real deal", it will probably behoove you all to become more familiar with its uses. It actually has a surprising amount of documentation and tutorials (for a free open source project).
First, you should probably learn about the
typical/normal use of hugin - stitching a couple different photos together in
order to create a larger photo or 360 degree panorama. For the basics, look at the first 2 or 3 tutorials on this page:
But what we're trying to do is closer to a "photo-mosaic" than it is to a "panorama".
These three tutorials seem particularly relevant, though it may not cover everything that we will need to do.
Some thoughts for moving forward.
1) it appears to be important that the control points for stitching the photos together all lie on the same plane -- e.g., close to the the water's surface. I'm not sure if the control points for the vertical and horizontal line segments also need to be on this plane, or if it's good enough that they're on a plane parallel to it.
2) I think we need to calibrate the cameras, so that we can settle the "v" (camera's horizontal field of view) and "b" (barrel distortion) parameters permanently, and get more consistent/accurate optimization results thereafter. There seem to be a couple of approaches to calibration, but we probably should try to take several photos of a nice regular grid. Or maybe some of our floor tile shots would be good enough, if they cover enough of the picture and the lines between tiles are dark enough to see.
Finally, here's some general information about different projections, in case you're curious what terms like "rectilinear" and "equirectilinear" mean...
All this said, I think it's important that some of us more deeply explore the various 3D stereo and 3D point-cloud modeling type software programs, in case they provide a better method than photo-stitching software like Hugin.