Does a high-pitching-moment symetrical airfoil exist?
What you probably look for is a symmetrical tail airfoil which produces high control moments. Since those moments are the product of force and lever arm, placing those control surfaces far from the center of gravity produces high moments.

A symmetrical airfoil will have zero pitching moment around its quarter chord point in attached flow. This is understood as zero pitching moment, since the pitching moment of an isolated surface is per convention defined around its quarter chord point. For a thorough explanation please consult this answer.

If, however, you choose a different reference point for your moment, even the symmetrical airfoil can produce a pitching moment. That effect is used in tail surfaces and for a given geometry, a higher maximum lift coefficient will produce a higher maximum moment. Traditionally, the NACA four-digit range of airfoils starting with a double-zero have been used for tail surfaces, but more modern designs will produce a higher maximum lift and lower minimum drag. A good choice would be the Wortmann FX 71 range of airfoils, like the FX 71-120 or the FX 71-L-150 which can often be found on gliders.