Fitting ODE models: best/efficient practices?

I have a sample run here, might be of interest to @wds15 et al.

Problem is a 2x2 orbital mechanics problem with unknown measurement error, masses and initial conditions, with only the position being measured. In the figure, green is the incremental warmup, black is the regular one up to the relevant time. For the wall time, x represents total time (warmup + sampling) and _ just warmup, everything per chain. Any run that took more than a 100 seconds was canceled. You can see the true and predicted trajectories and measurements at the bottom.