You don't say whether the amount of fog you are seeing after the 2nd developer is objectionable or not. Upon projection are the results unsatisfactory? I say this because you are using both a film and a developer for purposes for which they were not designed. Perfect results may not be possible. When the company dr5 was doing reversal processing certain films were not recommended for reversal.
For best results, the amount of silver halide solvent in the first developer must be carefully adjusted for each type of film you are reversing. Sodium thiosulfate does not work as well as potassium thiocyanate to clear the highlights. Developers specifically designed for BW reversal processing use thiocyanate rather then thiosulfate.
Have you tried using a chemical foggant rather than re-exposure to light? While it is hard to have too much re-exposure it is possible. A simple 2nd developer using sodium sulfide will act as a fogging developer. You might get better results with chemical fogging.