New update!
1. My son has finally undergone testing by a private psychologist to see what is going on with his writing. She's writing up the report, so we don't know the results yet, but we're hopeful we'll get some useful information out of it.
2. Private tutoring is going well. He's been there for several months and he's enjoying it a lot. We are considering adding on an extra day per week during the summer because he enjoys it so much.
3. He wanted to learn about chess, so we signed him up for the online chess club at CTY. There were no in-person chess clubs I could find for our area. We have no wish to overload him, so that's all we are signing him up for.
4. He did not get the best grades towards the end of the year because I stopped making him do pointless homework. It was leading towards frustration all around, and I saw no need to push him on it. I told his teacher as much, as well.
Thanks for all of the advice. I'll come back when we know the results.