Yes, appeal. Your son is learning that sometimes well-meaning people disagree and people like him get stuck in the middle. By requesting an independent review, he's helping all parties involved learn a little.
If "project part two" is a good idea, he should take it on, just for fun. In fact, since he's so young, and he has one conservation project under his belt, have him look into the Hornaday Award. It and Eagle Palms are great "next steps."
All members of the EBOR should have been volunteers, or functioning in a volunteer capacity. Typically at least one is not with the unit
You can look up the particulars by looking at the Guide to Advancement (PDF - Google BSA Guide to Advancement)
Section 220.127.116.11 references Particulars for Eagle Scout Rank
Section 18.104.22.168 Appealing the Decision
I'd focus on this more. Let your son know that not everyone will always agree. That not everyone always follows the same rule book. That his project was different, but that does not make it bad. It just makes it hard for some people to understand.
I'd do anything I could to change the perception of failure to a perception of something that needs to be overcome.