Okay, I think I figured something out. The first eight bytes are 32-bit integers. I'm pretty sure the first corresponds to the number of "parts" the model has, but the second I'm unsure of. After that are coordinates of points as single-precision (32-bit) floats, in the order X, Y, Z, X, Y, Z, …. The aforementioned "parts" mentioned before are separated by "FF FF FF FF". As for what determines which points are connected to which, I'm not sure. That would likely use integer values, but there aren't any non-float values other than those two integers at the beginning and the FFFFFFFF that separates each part. I don't think the order in which the points are listed affects it.
However, the apparent lack of any information related to which vertices are connected made the term "point cloud" come to mind. And then I realized: perhaps that's what PTC stands for.
One more thing: it seems the models' filenames are hard-coded into LabVIEW.exe. Which means it wouldn't be surprising if it can't load model files that it's not already programmed to load. However, I did find this humorous string, presumably used for debugging: "This model doesn't know how to see it's [sic] shadow. Two more weeks of winter."
But seriously, LabVIEW's support for custom control graphics is just terrible. It's almost a joke: the only supported formats in which you can load in images (as opposed to only being able to use specific hard-coded images built in to LabVIEW) are all non-scalable raster formats. There is one exception, but that exception is Windows metafiles, and that format just sucks. And if they're going to program in 3D support, why not enable importing of models as well?
EDIT: Apparently it also supports PICT images, which also support vector graphics. But that's yet another obsolete format that nobody uses. And some format with a ".aaa" extension, which I know nothing about. I only suspect that because ".pct" and ".aaa" are found as strings near ".wmf" in LabVIEW.exe.