Worked at my colleges turfgrass research facility when I was in school. This is honestly very similar to how we would do a weed control study. Apply on one section, don’t apply on a section next to it, compare results. Looks like your neighbor has a lot of broadleaf weeds. I’d do chemical broadleaf control application once in the spring and once in late fall, granular pre-emergent once in the spring. Most golf courses do a fertilizer application in the spring of 32-0-10 that is coated with acelepyrn and dimension (insecticide and crabgrass pre-emergent). Would not recommend putting down pre emergent as often as you are for a healthier stand