Being derivative free, this solver must estimate an appropriate step size. The solver has bounds of order 360, and a 0 initial guess, so it may be having great difficulty finding an appropriate step size heuristically.

You could try providing a typical step size as described in the docs. https://nlopt.readthedocs.io/en/latest/NLopt_Reference/#initial-step-size.

So it can take steps which have the resolution to detect the solution.

(A better initial guess will always help also).