Emergent communication (EmCom) with deep neural network-based agents promises to yield insights into the nature of human language, but remains focused primarily on a few subfield-specific goals and metrics that prioritize communication schemes which represent attributes with unique characters one-to-one and compose them syntactically. We thus reinterpret a common EmCom setting, the attribute-value reconstruction game, by imposing a small-vocabulary constraint to simulate double articulation, and formulating a novel setting analogous to naturalistic inflectional morphology (enabling meaningful comparison to natural language communication schemes). We develop new metrics and explore variations of this game motivated by real properties of inflectional morphology: concatenativity and fusion. Through our experiments, we discover that simulated phonological constraints encourage concatenative morphology, and emergent languages replicate the tendency of natural languages to fuse grammatical attributes.