well... I work in a shelter setting, what we do is put paper ON the grate, it keeps the poo off, and its alittle easyer on their feet when they want a hard surfice to walk on. but if we get poo on it, we ... well.. we have an industrial dish washer, we blast it with hot water, scrub then wash again.
What you might want to do is get a second grate and rotate them out, clean one, soak it if you have to over night then scrub, and during the next cleaning, just switch them out. (Bird poo is VARY hard to get off any kind of surfice)