Fitting a fixed nonlinear ODE model to closed-loop greenhouse data: which estimator avoids the controller-induced bias?

I have a physical greenhouse climate model, a fixed set of 28 ODEs with about 200 parameters, and a season of five-minute measurements from a real greenhouse: air temperature, humidity, CO2, plus every actuator setting and the outdoor weather. The greenhouse was controlled the whole time. A climate computer set the heating, vents and screens from the same measurements I am fitting to. So the inputs are correlated with the disturbances. Forssell and Ljung (1999) show that output-error fitting is biased on such data unless the disturbance does not reach the inputs. What I did: eight parameters as multiplicative factors on their defaults, bounded least squares on the simulation error (output error, no noise model) over twelve windows of eight days, three compartments. A fourth compartment held out. Result: temperature MAE 1.8 C on the hold-out, worse than a naive "same time yesterday" predictor at 0.7 C. Residuals are strongly autocorrelated (integrated autocorrelation time about 18 steps at 15 minutes). One parameter is not identifiable. The hold-out prefers a four-parameter fit over the eight. The question: for a fixed nonlinear ODE structure and closed-loop records, which estimator would you use instead of output-error least squares? Prediction-error with a fitted noise model, multiple shooting, a Bayesian fit over the factors, or something that uses the known controller? Any pointer to a worked example on a physical model would help. The benchmark the model serves: https://…