So another option could possibly be a montessori school (not sure if this is financially or geographically an option for you).

Kids have mixed results in Montessori and we have had both experiences (two different schools). First school I thought was amazing but it just didn't offer enough to her for her to be happy & she cried about going. We moved 1/2 way through the year and put her in a Montessori in our new state. This one has been running for over 50 years and goes through 8th. She is definitely being challenged in her own way and they are putting her a year ahead next year (still mixed age class but they have different base expectations for each year). She is SO eager to go to school every day & loves it. She has social interaction with kids 2 years older every day.

Just wanted to throw this out there incase this may be an option for you!