Nice to hear this is, on the whole, a more positive school experience than the last one!
The CogAT is not exactly an achievement test, but of course, all tests are to some extent measures of one's experience. It has widespread use as a group-administered aptitude measure, with all the pros and cons of group administration. The MAP is definitely an achievement test, but one should be aware that it was designed as a monitoring tool, rather than a comprehensive achievement measure, and that, depending on what version is administered, the ceiling for 2nd graders is likely to be fairly low for a child like yours. In any case, once scores get up into the ceiling of any test, a couple of raw score points difference can generate a percentile difference larger than one might imagine.
As to testing outside of the school-based screening (CogAT/MAP), my rule of thumb is that there are typically two main reasons for pursuing individual evaluation, such as cognitive (IQ) or achievement (or neuropsychological, which typically encompasses one or both of these) assessment.
1. In order to answer a specific question or problem, including obtaining information necessary to design solutions. In the context of GT learners, some typical presenting problems might include disruptive classroom behavior, or sadness/school avoidance, or apparent inattention/distractibility (among many other possibilities).
2. In order to obtain access to a service believed to be necessary. Typically, this would be a GT program or school, perhaps an extracurricular program (e.g., CTY, DYS).
From what you've described, it appears that while there is not a glaring category 1 reason for testing, there is a collection of smaller questions that might lead you in that direction. A category 2 reason for testing would depend mainly on whether the GT program is actually worth being in for your child specifically, which would require a bit more research on your part. My inclination would be that, if there isn't going to be opportunity to find out enough about the nature of the GT program before the timeline for obtaining all of the required qualifying testing passes, then it would probably make sense to go ahead and do whatever testing they offer, so you have as many options as necessary once you do know how the programming looks.
Of course, this also depends, as others have noted, on how your child would experience two or more hours of testing (most likely individual cognitive assessment) beyond MAP. Many high-cognition children find it quite entertaining, as it's one of the few times they are allowed to take their engine out on the racetrack and really floor it. Others, who might have more performance anxiety or perfectionism, may not find it as enjoyable for the same reason; they might have the unfamiliar experience of getting some items wrong.
And if your child finds philosophy to be an effective way to understand a healthy dynamic for him in his community, then by all means, read him philosophy! Giving only rules to persons who crave reasons is not conducive to compliance--nor does it ultimately engender real empathy and compassion.
(BTW, I love Eagle Mum's little story! If he had tried to tease out mixed dominant individuals (vs bi-hemispheric), and also investigated the long-term stability of dominance through the primary years, he could have added even more hours to his interesting data collection process!)
