I live in the Biltmore area and the elementary/middle programs that come to mind which tend to attract HG+ kids, roughly in descending order of proximity, are REACH, Madison Traditional Academy, Biltmore Prep (Spanish immersion), Simis/Meadows, Benchmark, Archway/Veritas (a Great Hearts school), and SUSD which now has a self-contained program at Hopi Elementary.

My YS is in his second year at REACH and we're thrilled with the program. I'd be happy to chat more if you're interested.