The Pyrocat developers all have the necessary ingredients to develop paper. When used on film as Sandy King proposed, they are highly diluted, high pH , low sulfite solutions. If you consider what you might do to make, say, Dektol usable on film, you could dilute it or lower its pH or both. The other way round, then, you could increase the concentration of the A solution, add some sulfite to the working solution, and see what happens.
Pyrocatechin and hydroquinone are like twins with different-colored hair. It is not pyrocatechin that uniquely makes Pyrocat a tanning, staining developer. Hydroquinone would do so as well, but with a different color of stain. The stain color of pyrocatechin is particularly desirable for negatives intended for printing by certain "alternative" methods. Sulfite is the great stain remover in pyrogallol or pyrocatecchin developers, so little is used. In fact, the Pyrocat series in glycol have none.
Now if the stain is the prize to be gained, the short developer life is the penalty. Otherwise, I don't see how the use of pyrocatechin will benefit. Pyrogallol can stand considerably more sulfite and still produce some stain, but most of us don't want our hands in pyro developers.