you can build a greenhouse unto the hillside (halfway between walipini and earthship). then have a sealed area, like a compartment of the greenhouse (like with a sealed glass wall and glass doors) which leads to a small, dry part of the greenhouse. this leads into your cave... you can hide the door into the cave by building a wardrobe around it... it s common for people to disappear by walking through a wardrobe... to Narnia or something....
Instead of slip form stone you might use rammed earth, maybe mixed with some cement (like clay-soil-cement oder cement stabilized compressed earth blocks)
i think, you would need an electirc dehumidifier inside your cave, alongside with other measures to reduce air humidity
i still think, a camper would be the best option