I can’t say I have tried to make a log with different side and end materials.
If you are not having much luck with the COOR wrapping and projection values or the VERT coordinates, then I would simplify it by having separate (very thin) CPRISMS (or other shapes) ate the ends of the log.
You can then control the materials separately for the ends ant the main log (sides) and may find it a little easier.
Versions 6.5 to 22
Dell XPS- i7-6700 @ 3.4Ghz, 16GB ram, GeForce GTX 960 (2GB), Windows 10
Dell Precision M6800 - i7 4700MQ @ 2.40GHz, 16GB RAM, AMD FirePro M6100 (2GB), Windows 7 64bit