I think a lot has to do with the individual psych. The psych who tested my son had limited experience with gifted - mostly LD. However, he was very good with my son and I feel very comfortable that the results were as solid anyone could have gotten at the time.
That said - yes, you should have your son retested. Make sure you meet with the psych ahead of time and bring copies of results of prior tests and your concerns about them. My understanding is that a second round of WISC so soon after the first round wouldn't be considered accurate.
It isn't unusual to have to do something at home to encourage your child to continue their interest in learning. Just an idea, but Highlights has several publications such as Puzzlemania that challenge the mind but don't necessarily feel like school work. That type of thing is often more productive than teaching them something that they will have to suffer through in school later.
Most school districts aren't in favor of skipping - even when close to the age cutoff. However, many times if you go with a private school for a year - and do a grade skip - you can return to public school without the grade skip being questioned.
