Just going on the basis of your scores, I would say yes, you should probably look further. Keep in mind that his relative weaknesses are still in the High Average range, so when the SLP looked at him, of course everything came out within normal limits. But it is highly unusual to have a 41 point difference between VCI and VSI, and a 31 point difference between VSI and FRI. (I would be less concerned about the WMI and PSI, as High Average scores on those indices is not that unusual in gifted kids.)
So one of the things that comes up is that on the FRI, most people use both verbal and abstract-visual problem-solving strategies. In fact, there is an element of needing to integrate the two to solve some of the items. His FRI may reflect the gap between his VSI and VCI, as he may have had items where his verbal reasoning was the limiting agent.
Another possible interpretation to consider is that his verbal abilities really were underestimated because he did not interpret the tasks conventionally at the beginning, but after the teaching items he figured out what the task was supposed to be. That probably still does not explain the whole difference between VCI and VSI, though.
And finally, anxiety/perfectionism is not unusual in gifted kids, nor is it unusual in LD kids (at least the anxiety part), which clearly makes it particularly not unusual in 2e kids. The awareness of one's own asynchronies can be very stressful, but especially for the very young, who are not emotionally-equipped to navigate them alone in a conventional environment. (And kindergarten is extremely conventional.)
