I've just been pulling it repeatedly. It does seem to reduce it year by year.
-- I don't think it has male and female plants. If I'm late on pulling it, then ALL of the plants set thorny seeds. There don't seem to be any seedless male plants.
-- It's important to pull it ALL early in the season, before it sets seed. Here the ideal time is June. The taproot usually comes right up with it. If I miss some and have to come back later when it has started to set seeds, there are two problems. One is, you can't really pull it with bare hands after it sets seed, and the other is, the seeds may fall off while you're pulling it.
-- I never go barefoot outdoors here (because my feet get painful cracks if I do) but goathead thorn seeds have a clever tactic of sticking to the bottom of shoes, or any item you might set on the ground outdoors, and then they come indoors, leap off, and wait to get under your bare foot. Like nothing else!
-- Around here they grow in empty desert, especially if there has been a little rain, so I don't think I can grow competitors. I'll just keep pulling it, a couple of rounds per season. If I've ever been tempted to think of round-up, it was not for goathead, because it comes up so easily when pulled early enough in the season. Round-up would only kill the plant whose leaves it coats, which pulling does as well; if there are already seeds on the plant, I don't think round-up would kill the seeds; and I don't think goathead thorns are perennial so I think if you get the taproot up, you've done it.