Yep. Do not UVW Map - just Unwrap UVW.
By using UVW Map, you're overriding the existing, working map, with an entirely new one based on the current shape of the object, which is what (censored)s everything up in the first place.
I felt so incredibly dumb when I found that one out (also after asking). 
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There are places though where the UVW Map IS the tool to use, followed by using the Unwrap UVW Tool in the same stack. It specifically excels at box mapping, so, if you have a model that is roughly cubical in shape, you can use the UVW Map to "box" map the object. Keep in mind that the ability of the UVW Map tool to make a good box map directly correlates to the size of the texture and the size of the object. For example, if you have a 512x512 texture, the UVW Map will make a decent looking map for a 1000 unit (u) cube since the default scaling for that size texture is 1001u x 1001u.
Where is Estelindis when you need her, she's so much better at explaining this stuff than I am. Anyway, here goes...
You'll see the image the cylinder tank from the BioWare Granary. We'll assume the texture is 512x512.
1. Note that I have added a UVW Map and have "box" checked (circled in red).
2. If you look below to the next red circle, you'll see settings for length, width and height. These correlate directly to the size of the map on the object (in actuality it IS the size of you object in the X/Y/Z planes).
3. Under those parameters, you'll see parameters for U Tile and V Tile (ignore W Tile it changes nothing from what anyone can discern). These parameters define the size of the object on the texture. A setting of 1.0 maps the UVW Map of the object to 100% of the texture. A setting of 2.0 would map the UVW to 200% of the texture - tiling the texture so it is now 1024x1024. A setting of 0.5 would map the UVW to 50% of the texture - scaling the object to use only a 256x256 portion of the texture beginning from the lower left corner.
4. Now, looking at the next image, I've applied a Unwrap UVW modifier to the object - at the top of the stack - and opened the UV Editor (the window to the left of the object. You'll notice that the box map is pretty spot on at the 1.0 setting for the U Tile and V Tile.
5. From this point, you can now use the selector in the Unwrap tool to adjust the mapping to suit your needs. WHEN FINISHED, SELECT ALL THE T-VERTS IN THE UV EDITOR AND HIT CTRL-W TO WELD THEM TOGETHER. Welding t-verts compacts the file size.
6. Lastly, here's my completed UVW Map. You'll notice that I squared of the top portion of the map, then moved the bottom-most row of t-verts down. This caused the texture to tile, making a band appear around the bottom of the tank.
