I have gravity-flow water lines connected to drippers, 5 gallons an hour, and the minerals in my water plug them up within 6 weeks or so. I never bury the drippers because if one of those drippers plugs up unexpectedly you won't know it until your plant starts to die. If it's a fruit tree or a blackberry vine you will have lost a lot. I've had gophers bury lines and shove so much dirt into the dripper it clogs up, but I didn't see that because it was buried.
I always keep the drippers up where I can watch them, and use the biggest ones I can so I don't have to wait an hour for the plant to get what I planned for it. If it
should get a gallon, I let it run for about 15 mins with a 5 gallon/hour dripper. I have had to pull out those drippers from the line, and suck and blow on them so many times, spin the tops around to break up the minerals, it's a lot of work.
The issue with the air space/negative pressure, I just open the ends of the drip lines and let it run out for 30 seconds, you'll hear the air come out. If the drippers are clear and up on top of the mulch. you'll hear the air spitting out of them. You'll have to watch how long of a line you can have open so your pressure works for the length of it. Be sure to watch the end of the line, not just the start of it, because that's the farthest spot that often doesn't get
enough water.
An important distinction: Permaculture is not the same kind of gardening as organic gardening.
Mediterranean climate hugel trenches, fabuluous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.