First of all, the [static] tag is only there to simplify a dynamic equation for Dynare. It must still be the same equation, but just in steady state. You cannot provide a different equation as you do. That is why you get an error. The reason your equation is different is that Dynare’s deterministic steady state refers to all declared exogenous variables being 0 and constant for all time periods. Dynare does not know the difference between shocks you want to set to 0 and ones you want to keep (the idiosyncratic one).
You say
But Dynare cannot do this as the deterministic steady state is defined as one where all shocks are 0 and expectations drop out. That’s why I recommended to define the term involving the expectations as a separate endogenous variable in some other post.
Also, I already told you that if you want Dynare to “accept” the values you provide as steady state values without checking their correctness, see [Approximate around user provided values)
Lastly, I am not sure that Dynare can solve your type of model. This is a very peculiar and singular type of issue where you seem to be the first one ever considering it. Thus, I cannot provide much guidance and you are mostly own your own. Good luck.