We had several round of discussion on this and I think the only actionable recommendation for general users is to try and profile.
one could limit the model to the first few time steps at first (during warmup?) , to not waste so much time on regions in the parameter space that are hopeless.
I’ve tried this, and the peril is the shortened model may not provide sufficient likelihood information to influence the posterior, leading to inaccurate warmup, or even making warmup taking longer time.
However, even for moderate accuracies, the flow of the system should not actually change too much.
There is no guarantee on that. There are many ODE systems evolve dramatically differently according to how accurate we solve them.
In general controlling ODE solver with sampler performance in tandem is not fully studied. The latest manifestation of this uncharted water is @wds15 's work on adjoint ode solver where we simply don’t know how controls will affect the performance, and the next best solution is to release an experimental version so people can try it.