To substantially reduce cable taper--if we reach a point where mass produced graphene powder (but not solid graphene structures) is economical--an extremely strong material like carbon fiber or UHMW might be impregnated with graphene powder for enhanced strength (and other attributes such as creep resistance). Another means to keep cable taper reasonable may be to attach hydrogen balloons (perhaps with a helium liner) along the sides of the cable (that are capable, via telescoping arms perhaps, to fully or partially detach to permit vehicle travel).

The cable length might also be supported in space by nuclear or electric spacecraft pulling on it (being fueled or electrified via elevator cable) to further reduce taper and/or permit more/heavier traffic.