I’ll try it out later (y).
In the meantime I’ve got a comparison for anyone interested. An orbital mechanics problem with pretty wide priors, similar to what is discussed here Fitting ODE models: best/efficient practices? - #63 by Funko_Unko
Comparing the adjoint method with different backwards tolerances with the rk45 and bdf methods. A model, problem and method description is at the bottom of the image.
Take everything with a grain of salt, sometimes there are some divergent transitions. I’m not 100% sure why.