Is $3,200 to install 6-inch gutters a fair price?

I just bought this new construction house in December, and it's still under builder warranty. My current 5-inch gutters are not sufficient due to a large sycamore tree shedding leaves and twigs constantly, and frequent windy, stormy weather in the Midwest. I clean them weekly, sometimes multiple times a week, but they still fill up and overflow during almost every rainstorm. The substantial incline of my yard makes ladder use sketchy, despite using stabilizers and other tools. I'm looking for advice on whether to go with 6-inch gutters or wire mesh gutter guards. The 6-inch gutter quote feels steep for a new homeowner, and I'm wondering if the builder warranty might cover it or if the estimate is negotiable. While I've heard mixed reviews on mesh guards, even reducing my cleaning frequency would be a win. I'm also considering trying cages with regular leafblower/hose maintenance and am interested in extra wide downspouts.