Angular fragment distributions from the dissociative recombination (DR) of HD(+) were measured with well directed monochromatic low-energy electrons over a dense grid of collision energies from 7 to 35 meV, where pronounced rovibrational Feshbach resonances occur. Significant higher-order anisotropies are found in the distributions, whose size varies along energy in a partial correlation with the relative DR rate from fast-rotating molecules. This may indicate a breakdown of the nonrotation assumption so far applied to predict angular DR fragment distributions.