I assume that the ground is either sand or poor soil or a mixture of these, and is quite dry most of the time. Not sure why you say the earths are only 1 m deep ; is this as far as they can be driven before hitting rock?
One method is to run the earth grid to a place where the ground is damp all year like a river bed or swampy area and install at enough depth to ensure all year moisture around the grid.
Another is use concrete which is a fantastic way to earth. Connect to the reinforcing steel in building foundations and piles. Piles are really good if they are deep. Dryness might be a problem with surface foundations. Also the building slab, if concrete, and installed on grade (on the ground surface) and it is not insulated by waterproof membrane, can also work well as moisture retention under a large slab can be quite good, although if really dry, even this could fail.
Another answer might be deep rods. For instance, on the site I am at in Qatar, the earth rods pilot holes will be drilled to depths of something like 30 m to find the summer water table, and multiple rods installed to reach 1 ohm resistance. Here the ground is lime rock after about 500mm and the surface super dry. Only the deepest end of the rods really do anything useful.
Your rods need to reach something consistently wet in the undersurface and again only the deep ends really do the work. Can't help with how to install deep rods in sandy soils.
The one that I think might work the best is deep rods. This doesn't require considerations like whose land in the swamp on and is it corrosive in there, or will the structural engineers like their concrete/steel being used for earthing.