K.S.
You don't mention what other social outlets your son has but how about....
Independent sports (gym membership, swimming, biking, marial arts). There is so much going in in the body of a 12 yr old boy...A physical release, learning physical control and patience might be good.
Team sports (maybe an association outside your school district giving him an opportunity to meet new kids)
Church youth group
Community Ed...But don't sell it as more "school" they have some great offerings.
Mom time...I understand with 2 other kids it would be hard but can you find time to roam the library, the mall, grab lunch, take in a movie -- Just you and him?
Make over -- I know this sounds silly for a boy but I am the mom of boys and they really do care (tho no where near as much as girls) about having cool clothes, cool shoes, or a really cool hair cut.
Grampa/Uncle time -- My brother had some similar struggles and no one could bring out the hidden side of him quite like our uncle and our grampa.
Is he your oldest? You mention your ex is less than happy about the split and he is perhaps feeding his dissension to your son? A 12 yr old who has to listen to adult complaints would definitely feel miserable. See if he can get some mild talk therapy.