Optimization methods for fitting ODEs

TL;DR: Anyone have a recommended optimization method for fitting ODEs to
data when I have the analytic gradient?

I am currently fitting the numeric solutions of ODEs to data. I wrote an
objective function, a gradient on that objective function, and passed both
to scipy.optimize.minimize. This worked fine on small problems, but all the
scipy minimize methods broke down when the number of parameters got large
(~40). My past experience in Matlab suggests that this happens because some
parameter directions are MUCH more tightly constrained than others.

The scipy methods are easy-to-use, but I was wondering if there were any
alternatives that people had found to work well when the problem got too
hard for scipy. Here is a list of features that I probably need:

* black-box optimizer
* local optimizer
* uses supplied analytic gradient
* allows bounds on parameters
* accepts a maximum step size

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