I believe what you have there is "False garlic". I have a lot of it. I haven't come up with any answers either. Anything with a waxy leaf is hard to kill. From what I have read it is a protected species. Google or check with your county agent.
I'm a grasshopper guy all the way. They do have a homeowner line. I've Owned 3. My current is a 900d. Yes they're pricey. They started the zero turn idea. If you have a question just call the factory they will be glad to help. Good customer service .