You cannot book a paid flight reservation at aa.com that doesn't contain at least one flight with AA flight numbers. Since JFK-ANC is only sold as AS flights that is why it's not showing up.

Just book the flights directly with AS, you can do it as a guest, enter your AA# in the frequent flyer field and your TSA redress number and everything will carry over. AS will know your status.

For mileage earning, keep in mind that AS flights post by distance and booking code, not fare paid.