Welcome, jenjen!

I am no expert, but DS5 also took the WJ-III Ach. around the same age. Those are very strong scores, and nice and even between math and reading! I don't know that I'd worry too much about his writing at this age - DS's tester did not even administer writing because he was so young.
Did the tester give you "broad scores" (I think they need to do the math and reading "fluency" subtests to calculate those)?
DS took the WJ a year ago now and his reading was higher, but his math was lower (to be fair, I did not expose him to much math until this past year, and my guess is that DS's scores would be MUCH higher today). DS is attending public kindergarten and there is NOT a great deal of challenge for him (and I doubt there would be much for your DS either, without modifications). Still, the program is half-day so we do work a bit at his level at home (we do our own "homework" at his level since he hasn't needed to practice letter sounds, counting or sight words). I also give DS's teacher some credit, because she has tried to add some "challenge activities" for DS this year at school. In my experience, whichever school your DS winds up at, the individual TEACHER can make a HUGE difference. A flexible teacher that is willing to add differentiation when needed can REALLY help a bright child make progress.
Do you have gifted schools in your area? He may qualify for those. Does your local school have a gifted program? Unfortunately, many of those programs do not start until 3rd grade or so, though (we just went though this with DD8). This may help add some challenge for him, too. I think, as parents, we too need to be flexible and willing to change programming, or even schools, if something that was working is no longer suitable for our child.