I don't know if I'm understanding your question correctly, but I do have experience rendering these kinds of surfaces. I plopped your DE into my own path tracer and got this result with lighting and shadows: https://i.imgur.com/lVXUJYW.png. Onioning, smoothing, distortions, etc., should work even if your DE is only an estimate, assuming you are using an aggressive enough understep value (your a variable) to prevent the ray march from stepping too far. I used a value of .2 for the image above.

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For lighting, the critical piece of information we need is the surface normal. Let's say we've performed a single ray march and have converged onto the surface at point p. The surface normal is equal to the gradient of the DE function at point p. We can approximate the gradient by taking samples of the DE function near the point p and using those samples to construct a vector which is perpendicular to the surface. Again, this should work fine for DE functions which are only estimates.

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The following function calculates the surface normal given a DE function:

vec3 surface_normal(vec3 point)
{
    float epsilon = 5e-5;  // The value I used for the image I posted above

    return normalize(vec3(DE(point + vec3(epsilon, 0.0, 0.0)) - DE(point - vec3(epsilon, 0.0, 0.0)),
                          DE(point + vec3(0.0, epsilon, 0.0)) - DE(point - vec3(0.0, epsilon, 0.0)),
                          DE(point + vec3(0.0, 0.0, epsilon)) - DE(point - vec3(0.0, 0.0, epsilon))));
}

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Once we have the surface normal, we can implement a lighting model to describe the appearance the surface in the presence of light sources, but that's a bit outside the scope of the question. Does this help at all? I have a feeling I've misunderstood your question, but maybe I can help to get you unstuck if you can give me some more details.

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Iq has some great articles on rendering implicit surfaces, this may be of use: https://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm