Hi TCG. Looks fantastic, you wouldn't believe it was a cheap kit from the photos.

Re. neck thickness. I just did exactly what you are contemplating with a TL kit I have just finished. Guitar all put together, neck finished with tru oil and I just couldn't take to the baseball bat so I took the neck off and went at it with a rasp and sand paper. Very carefully and nervously!!! I first took off a flat area across the back down to 20mm at the first fret and 21.5mm at the twelfth fret. I then rounded the profile using two cardboard cutout profiles I made from another guitar with a profile I liked. Lots of sanding with various grades later it felt to be the right shape. I re-finished with tru oil which blended in perfectly with the existing finish.

The neck feels and plays much better now. I have had no problem with the truss rod (that was an area of concern) but only have 9's on.