Compost socks, aka silt socks, are basically long tubes filled with compost, you see them around construction sites to control erosion. Although they are generally made from mesh material, landscape fabric can also be used to better restrict root growth and prevent weeds.
They have been used to grow strawberries and other fruits and veggies, but figs really shine when planted in them, the growth first year has been equal to planting a tree in fertile soil.
Compost can cause drainage problems in container mixes, but when used in compost socks it acts like a small raised bed. It can provide adequate fertilizer for the first year, and holds more water than potting mixes, simplifying care. To enhance growth in future years, holes can be made to allow some roots to grow into the soil.
Irrigation is easy, soaker hoses or drip tape work well, as would sub irrigation (compost has good wicking properties). Storage is no more difficult than standard containers, in fact, they are cleaner and can be stored on their sides without spilling any compost. If indoor winter storage is not an option then they can be tipped sideways and covered in their growing locations.
Rather than shuffling them in and out during early spring they can be laid on their sides and covered and uncovered.
Repotting these trees will take some ingenuity, but because fig trees are so resilient, there are several options that could work.
Here's a few pictures of growth progression, these were stuck in late April.