Psychoanalysis is a disciple not famous for doing experiment, we have Behaviorist using objective experiment data to verify/reject their hypothesis stimulus-reaction connection, and Cognitive Psychologist testing the strength of connections between various nodes in a schema. In my mind, it is yet for Psychoanalytic propose and doing experiments.
One of the experiment I suggested here is applying the logic from another article. In order to intentionally forgotten an negative-emotion-provoking object the Unconscious has to memorize what to forgot so Conscious would have difficulty in memorize that. Therefore, similar to how new radar system in detecting Stealth Airplane, if we could compare to the background detection rate of object, we could easily deduced that an object must be emotionally loaded when is unusually hard for a subject to memorize. I also speculate that the strength of emotion related to the object is positively correlated to the difficulty of memorization, which means we can objectively measure the effect of Complex.
Suppose after doing the proposed experiment that we already stablished the presence of Complex after the fact, it follow that since every science require the hypothesis to be predictive, we also need to demonstrate we could build complex using standardized procedure. We thus need to design set of experiments which we first establish the base rate as an indicate of effect of existing complex, do detail analysis of personality so to establish the standardized Complex-building procedure, then engineering an event that would definitely provoked a strong negative emotional event, and again measure the ease of memorization of different objects to measure how newly established Complex is taking its effect on Conscious, then ensure the complex is resolved through experimenter exposing those accident as a purposeful act to promote a desired effect, and then the ease of memorization of those different objects is again measured to verify the hypothesis that resolution of complex indeed restore the performance of memory on several emotionally-loaded subject.