One last thing: For some reason SH3D still imports the object files at a scale of about 100/1 even with Magnetism off--but as you said, it's easy to scale them, so I'll just not worry about it.

That is because Sweet Home 3D interprets a cm where Blender uses a mm (I think, might even be 1/10 mm, I'm not sure). You can easily scale when you check "Keep proportions" and add *10 or *100 to one of the size values. Sweet Home 3D will do the calculations.

I still have trouble figuring out how to select all the surface triangles, since there could be thousands and in a 3D view, it's not that easy to even be sure what you're clicking on. Seems like it involves a lot of painstaking work.

I still use the older 2.72 version of Blender but the latest version should not be too different. Hold Ctrl and you can drag over faces to select them, that way you can also drag an area around faces to select them.

One thing that I do not understand is, why SH3D maps textures in an unexpected way, when I'm not specifying multiple surfaces. I would expect that a 2-dimensional texture would be mapped to an object that has faces pointing in different directions (but not defined as separate faces) as if that texture was a thin sheet that gets wrapped around the object (just like when you wrap a car with some custom design graphics)

But instead the texture is applied so it faces correctly on ONE of the surfaces but then gets cut through like a 3D cake--which makes it look completely incorrect on all the faces that have a different orientation than the first one. I wonder who would ever want it to be done that way?
I assume there is no setting in SH3D that would change how textures are mapped?

Remember, Sweet Home 3D is interior design software, not 3D modelling software. What you describe is specifically 3D modelling. That means that Sweet Home 3D has no features for this but Blender does. You will have to 'fix' texture mappings with Blender.
What might be easier is to split your model into separate parts by exporting each part with a single material. Imported in Sweet Home 3D there are two ways to set a texture in the Modify Furniture dialog. In the Color and texture section you can choose the Texture button, this will set a single texture over all of the model. This will change the texture mapping and might be what you need. The other way is to click the Modify button in this section. That will open a new dialog where you can also set a texture. This will not change the texture mapping (If you scale, rotate, or shift the texture, it will change the mapping when you export the model).

Here is an example of a powder coated black metal texture. The object does not have different surfaces defined, and if I apply the texture to the entire object, only one face has it applied correctly. But if I wanted the texture to be applied correctly everywhere and wanted to be really detailed about it, I would have to define EVERY surface, including the inside of every single hole cut. That seems crazy. Why wouldn't SH3D simply wrap the texture correctly?

Sweet Home 3D displays the texture as it is defined in the imported model. If that is wrong then the mapping in the model is wrong: fix it in Blender before export (UV unwrap, select projection type). You can try the first method I described because that kind of does the wrapping around your model but that only works on a part or model with a single texture. You can even scale, rotate, and shift the texture.

With the things you want to do you will have to learn more Blender. As said, Sweet Home 3D is not 3D modelling software, although its capabilities have grown so much over time that you can 3D model a little when you keep it simple. There are people who have become quite adapt in creating 3D models with Sweet Home 3D but they so without things like texture projections and smoothing. I create most of my models using several steps of import/export between Sweet Home 3D and Blender, and sometimes some manual editing of the .obj and .mtl files.