In decentralized federated learning (DFL), substantial traffic from frequent inter-node communication and non-independent and identically distributed (non-IID) data challenges high-accuracy model acquisition. We propose Tram-FL, a novel DFL method, which progressively refines a global model by transferring it sequentially amongst nodes, rather than by exchanging and aggregating local models. We also introduce a dynamic model routing algorithm for optimal route selection, aimed at enhancing model precision with minimal forwarding. Our experiments using MNIST, CIFAR-10, and IMDb datasets demonstrate that Tram-FL with the proposed routing delivers high model accuracy under non-IID conditions, outperforming baselines while reducing communication costs.