The assembly of virus capsids proceeds by a complicated cascade of association and dissociation steps, the great majority of which cannot be directly experimentally observed. This has made capsid assembly a rich field for computational models, but there are substantial obstacles to model inference for such systems. Here, we describe progress on fitting kinetic rate constants defining capsid assembly models to experimental data, a difficult data-fitting problem because of the high computational cost of simulating assembly trajectories, the stochastic noise inherent to the models, and the limited and noisy data available for fitting. We evaluate the merits of data-fitting methods based on derivative-free optimization (DFO) relative to gradient-based methods used in prior work. We further explore the advantages of alternative data sources through simulation of a model of time-resolved mass spectrometry data, a technology for monitoring bulk capsid assembly that can be expected to provide much richer data than previously used static light scattering approaches. The results show that advances in both the data and the algorithms can improve model inference. More informative data sources lead to high-quality fits for all methods, but DFO methods show substantial advantages on less informative data sources that better represent current experimental practice.