Motivated by the intriguing properties of magnetic molecular wheels at field-induced level crossings, we investigate the spin-Peierls instability of antiferromagnetic rings in a field by exact diagonalizations of a microscopic spin model coupled to the lattice via a distortion-dependent Dzyaloshinskii-Moriya interaction. We show that, beyond the unconditional instability at level crossings for infinitesimal magnetoelastic coupling, the model is characterized by a stronger tendency to distort at higher level crossings and by a dramatic angular dependence with very sharp torque anomalies when the field is almost in the plane of the ring. These predictions are shown to compare remarkably well with available torque and nuclear magnetic resonance data on CsFe8.