If you haven't already, take your son and go and visit the schooling options. Have these discussions with those schools and give them a chance to explain what they would do for your child in his circumstances. See the classrooms at work. Ask if your son can sit in while you talk to the Head. The only way to get a real feel is to to be there.
If your DS takes up the option for the Gifted class there is nothing stopping you going to back to homeschooling or another option if it doesn't work out. We were worried about the workload when our daughter, who does not have your DS's particular challenges, went into a gifted class. Turns out they were very flexible about homework if you spoke to them. They were building skills but not at the expense of the child and their happiness.
Is part time home school an option? It is in some states and some situations but not all.
You need to trust your instincts once you have a feel for what the schools could provide. With a good IEP would it work? Would he have access to additional services at school? New friends? Different skills?
You are fortunate that home schooling has been working and it remains an option. I don't think it stops being an option if you try something new and it doesn't work.
