Yes, in general, not using initial values is to be preferred if it is possible. This, however, does not apply to this case and so you would have to go with a second best option and so either use a steady state file or compute it outside of Dynare and fill it in via initial values.
The approach in both cases is similar, like you mentioned, reduce the model as far as possible and then use a numerical solver to find the steady state. The way I do this is by trying to solve it analytically on paper and then reduce the system of equations until no longer possible. By then the size should be reduced, as for some variables it is indeed possible to find their steady states, and you should be able to use either fsolve in Matlab or the steady state file integration in Dynare.