The trait of oxygenic photosynthesis was acquired by the last common ancestor of Archaeplastida through endosymbiosis of the cyanobacterial progenitor of modern-day plastids. Although a single origin of plastids by endosymbiosis is broadly supported, recent phylogenomic studies report contradictory evidence that plastids branch either early or late within the cyanobacterial Tree of Life. Here we describe CYANO-MLP, a general-purpose phyloclassifier of cyanobacterial genomes implemented using a Multi-Layer Perceptron. CYANO-MLP exploits consistent phylogenetic signals in bioinformatically estimated structure-function maps of tRNAs. CYANO-MLP accurately classifies cyanobacterial genomes into one of eight well-supported cyanobacterial clades in a manner that is robust to missing data, unbalanced data and variation in model specification. CYANO-MLP supports a late-branching origin of plastids: we classify 99.32% of 440 plastid genomes into one of two late-branching cyanobacterial clades with strong statistical support, and confidently assign 98.41% of plastid genomes to one late-branching clade containing unicellular starch-producing marine/freshwater diazotrophic Cyanobacteria. CYANO-MLP correctly classifies the chromatophore of Paulinella chromatophora and rejects a sister relationship between plastids and the early-branching cyanobacterium Gloeomargarita lithophora. We show that recently applied phylogenetic models and character recoding strategies fit cyanobacterial/plastid phylogenomic datasets poorly, because of heterogeneity both in substitution processes over sites and compositions over lineages.