> No, that wasn't my opinion. If theta doesn't always determine the other parameters, then (1) won't work. If it does always determine them then the lower level solver should work 100% of the time.
I think you've misunderstood a little bit. I've actually run across any number of instances where there is a unique solution to a problem but a numerical solver fails. For instance, it can get stuck at a local optimum. So it will never be 100%, though I suspect for my application it will be close.
Anyway, theta uniquely determines the other parameters (numerically), so I'm going to keep working with approach (1) for now. Thanks for the advice!