Your goat heads sound very similar (at least in effect) to what we call "puncture vine" in eastern Washington. It may be the same thing--I don't know the botanical name. It's truly nasty stuff, and I remember using a metal strip inside my bike tires as well as puncture-sealing compound injected into the inner tube when I lived there. Even with those, tire-patching sessions were very frequent. The seeds of course get tracked everywhere because they stick in your shoe soles. You wouldn't want that kind of thing anywhere near any kind of inflatable pad! I guess I'd need a big thick foam pad (I have one for car camping) or 2 or 3 ridge rests, with hip and shoulder holes cut into the top one. Or maybe a titanium ground sheet?