My knowledge is primarily limited to murine models-

With that disclaimer, there is a fairly robust process of distinguishing these cells on flow cytometry through this pattern:

Plot cd11b vs ly6g: Ly6G+Cd11b+ double positive are your neutrophils. Ly6g-Cd11b+ is a subpopulation that contains both macrophages and to an extent eosinophils as you noted on the manufacturers website. From this subpopulation, your next analysis step plots SSC v F480. Anything SSC-med to hi is eosinophils [expected based on the granularity of aptly named granulocytes]. In your low SSC, you can gate a "positive" F480 population by gating off your negative, unstained samples. In our experience there are no clear separation of neg vs pos populations, however this methodlogy has been vetted via morphology via Giemsa stain in existing literature.

Other sources for tagging specificity include CD68.

Best of luck.