I am with you in the volume of displaced water giving the buoyancy. You need to assume some watertable level.
Respect what weight to consider counteracting it, your walls and slab and whatever standing weight sure to remain on it.
For safety you will need to assume the less deeper watertable you see likely to ever occur in the life of the structure. Assume it is say upwards but close of your bottom. You may want to count the water plus solids weight downwards and stabilizing, but hydrostatic prssure also acts upwards, what means that water weigh can't be counted as stabilizing.
Even more simply, the water around the lips of your slab can't help against buoyancy, otherwise we would see more of this in vessels (the water is free to flow around), AND any submerged solid particles in the soil are themselves subject to individual buoyancy, or if you want, the sum of its weight plus the own buoyancy gives... the submerged soil weight.
Say only 1 metric ton/ m3 able to stabilize against buoyancy your well contraption.
The non submerged soil could be taken at its natural weight, since not being completely surrounded by water the hydrostatic buoyancy has not yet developed, and the whole brunt of weight is passed downwards by contact between particles. It may be however wise to consider all the displaced volume as submerged for some cases.