Devices formed from single molecules attached to noble-metal electrodes exhibit large conductance fluctuations, which inhibit their development as reproducible functional units. We demonstrate that single molecules with planar anchor groups attached to carbon-based electrodes are more resilient to atomic-scale variation in the contacts and exhibit significantly lower conductance fluctuations. We examine the conductance of a 2,6-dibenzylamino core-substituted naphthalenediimide chromophore attached to carbon electrodes by either phenanthrene anchors or more extended anchor groups, which include oligophenylene ethynylene spacers. We demonstrate that for the more spatially extended anchor groups conductance fluctuations are significantly reduced. The current-voltage characteristic arising from long-range tunneling is found to be strongly nonlinear with pronounced conductance suppression below a threshold voltage of approximately 2.5 V.