Alright, I totally re-built the texture skin, it now works and looks much better, but I didn't just stop there - I realized that many people would like to easily create their own camo colors but don't have the expertise to re-plaster everything in Blender (the technique I used in the source file *is* compound and a bit complicated) and wouldn't want to study Blender for a year before learning how.
Therefore, I rendered the new skin in layers with alpha channel, and put all the layers into a GIMP file. Now all one has to do is open the GIMP .xcf (or the individual PNG files of the layers), click on one of the camo pattern layers, and select "colorize" from the menu. Adjustments to contrast and brightness before and after can also fine-tune the colors. Once doing this for all three layers of the camo pattern, presto! - A new soldier texture is born, with custom camo colors. There is of course also another layer for all the other parts of the skin (gloves, belt equipment holders, etc.), as well as a top layer that blends with the camo pattern layers to make cloth-like wrinkles and folds.
I'm really proud of this - now anyone can easily customize the model skin, without having to know a complex program like Blender.
Here's shots of the original (uncolored) GIMP xcf, and one example of a woodland texture.
Edit: BTW, these new skins are UV mapped very differently, they won't work with the current models in the SVN PK3 files (because they were re-done to fix and improve things). I will later update the SVN files, and this issue shouldn't interfere with any of the animations, so there should be no problems.