You will find carbon rods from zinc carbon batteries are unsuitable on the whole..too abrasive.
brushes are MOSTLY graphite with binders to control:- resitance, and trade off between wear rate and wear of comutator….
Even large brushes form say a low voltage motor might be unsuitable to cutdown for a mains motor..
I have used pure graphite (artist ) to make emergany brushes and the results less than ideal..very high wear rate of brush, filfthy motor and VERY high inrush current ( little or no resistance from brush)..
Sorry no easy answer but slight adaption of simular "rate" brush more readily available ( or cheaper) might be posible ..