I found dealing with goatheads require increasing the depth of penetration needed to reach the tube. That means:

1. heavy-duty commuter tyre with kevlar belt
2. Tuffy liners
3. thorn-resistant tubes with 3mm thick tube on outside

Combined, these give about 5-6mm of penetration resistance. The other thing is that goatheads never puncture immediately. They get spun around and around with your weight pushing on them to force them into the tyre. There are ways to scrape off the goatheads before they've penetrated deep enough to cause flats. Back when I commuted 25miles a day to work at the shop, I used to get 1-2 flats a week. After figuring out all the tricks, I get less than 1-2 a year.