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If you could spare a little room you could strap across with hat channel and screw the board to that. The bend in the channel should help support the board on the flat. In high humid conditions you might need the support over time. No saggage. Don't be tempted to screw it to the duct.
for best results with kichen soffits I usually frame them with plywood first it's cheap and you can glue and screw over it to get the most out a job that must be plumb and sqaure. sixteen centers on the ceiling and tenty four on the walls with half inch. twenty four on the ceilings and thirty two on the walls with five eighths more for both if backed up with bridging or plywood.