Here's a good list of articles on Hoagies, with a list of testers familiar with GT kids. I'm not so familiar with 2E, but maybe the list also IDs testers who are familiar with 2E kids. Psychologists familiar with gifted

Does your school have any sort of guidelines, rules, or experience with acceleration that you can refer to while saying that your child meets all the criteria? I'm not sure that outside testing will necessarily "force their hand" as you say. Some schools won't accept any outside testing. Before you get outside testing, I would make sure you know what the district will allow.

Also, the Iowa Acceleration Scale provides a nice objective checklist for whether a subject or grade acceleration would be appropriate. There is a lot of discussion of that on this board, if you do a search.