Shrinkage and poor measuring are typically not problems. This is very simple. You bring the material to the site in a loose state which means a low density. The material is placed and compacted which means a high density. It is all a matter of comparing the loose versus compact density.
I have done more of these projects than I count where we remove soil and replace it for various reasons. We prefer to proofroll with a loaded dump truck to locate weak areas or potential pumping. It has been my practice to begin backfill after the proofroll passes. I believe the more you dig...
There are several ways to support large above grade tanks. It has been my experience that the tank builders will want to elevate the tank shell by a foot or so above the ground surface. To accomplish, I recommend concrete ring walls. In this case, the tank bottom sits on the ground surface...
Regarding TDAA's comment to remove and replace the fill, it would seem to me that this suggestion is discounting the adequate performance of the remainder of the foundation on the fill. I guess I don't see as straight forward as y'all do.
I agree with Aeoliantexan on several of his points. Silts are OK if you can compact them properly. Thick lifts in silt are really a problem because of the narrow moisture band at the proper density range. Plus, there can be some amount of bridging that does not show up with thicker lifts...
If we think about the reason for specifiying soil density as a control mechanism for compacted fills, we might find that the SPT can be useful. The compacted fill will probably have to support a load even if it is its own weight. To support a load, the soil will have to possess a minimum shear...
There seems to be too many unknowns to make such a decision to just replace the old slab with a new one. You should have a geotechnical engineer do a proper investigation (soil borings & lab tests) and recommend a new course of action. It may be that a new slab can be placed but you they may...
More information would be helpful. The downdrag becomes an additional load to be resisted by the foundation soils. The geotech has to predict the load and the structural should make sure the foundation pile/pier can structurally withstand the additional load. If this is a fiction pile, the...