What about the Sparta being composed of half-orcs? Maybe humans and half-orcs..... It'd give half-orcs an interesting place in the setting, not just the offspring of Very Bad Things.
Perhaps a relic of some earlier era where orcs hadn't descended so far into uncivil barbarism, and some intermingled with humans of a respected militant clan or canton. Over time they separated from social and religious schisms, but the human/half-orc group continued to practice its ways and developed into this Spartan empire over time.
Maybe the Helots of this Sparta are orcs who were later conquered by the 'upstart halfbreed kingdom' and forced to humble themselves before their 'betters'.......and what began as simply an act to make distant, orcish cousins respect the newfound power of the half-orc/human alliance, devolved into a brutal oppression of those orcs after the next pair of Spartan kings took over......
Just tossing out an idea in vein of what others had been suggesting with hobgoblins.