Using event-by-event fragment momentum spectroscopy in a storage-ring merged-beams experiment, we find laboratory evidence that in the dissociative recombination (DR) of HCNH+ with cold electrons the energetic isomer HNC is produced with a high yield, similar to that of HCN. With a newly implemented mass-sensitive fragment imaging detector, we analyze the kinetic energy release of the triatomic fragments DCN/DNC from the DR reaction of the isotopologue DCND+ with cold (near 10 K) electrons. The results show that the internal energy of these fragments is extremely high, far exceeding the isomerization barrier between DNC and DCN. From this laboratory characterization of the DR reaction we conclude that also the triatomic fragment HCN/HNC from the DR of HCNH+ will carry a large amount of ro-vibrational excitation and show that this implies an isomeric production ratio in a narrow range near unity.