What is the intracellular chloride concentration in rat T-cells or thymocytes
Felber and Brand 1982 estimate the intracellular T-cell chloride concentration to be about 30 mmol, which seems to me to be on the high end for intracellular chloride in mammalian cells (though my experience is mostly with neurons, I'm not as confident of intracellular chloride concentrations in other cell types; for a neuron I'd expect &lt;10mmol). Still, that leaves a big anion gap for your SID estimate.
I think it is more likely that your SID estimate is simply wrong. The number you report sounds like an extracellular SID; Kowalchuk et al 1988 suggest intracellular SID is about 4X extracellular for muscle, which sounds about right for your situation as well.
Most of the intracellular anion contribution is provided by negatively charged proteins, amino acids, lactate, etc, rather than strong ions like chloride. Many of these are nearly completely deprotonated at physiological pH, though (for a typical amino acid the first pKa is ~2).

Felber, S. M., &amp; Brand, M. D. (1982). Factors determining the plasma-membrane potential of lymphocytes. Biochemical Journal, 204(2), 577-585.
Kowalchuk, J. M., Heigenhauser, G. J., Lindinger, M. I., Sutton, J. R., &amp; Jones, N. L. (1988). Factors influencing hydrogen ion concentration in muscle after intense exercise. Journal of Applied Physiology, 65(5), 2080-2089.