Steady state with changing parameters and fsolve

I am running some deterministic simulations in Dynare, and I would like to look at the effects of a change in parameters over time (for example, growth rates, demographics, and so on). However, due to the nature of my model, some steady state variables do not have a closed form expression, and as such I need to solve them numerically (with fsolve).

The question I have is: what is the best way to handle steady state computation for deterministic simulations? Should I go with providing a numerical guess (computed externally) using initval; or with either steady_state_model; or a _steadystate.m file? How to handle this problem when deep parameters are changing over time, particularly when the fsolve routine requires these time-varying deep parameters as inputs?

For example:
initval; a = a_initial; n = n_initial; end;
where by _steadystate.m contains:
options[...]; %solver options
ss_vars0 = [1,2,3]; %initial guesses
ss_vars = fsolve(@(x) find_steady(x,...,a,n,...),ss_vars0,options);
R = ss_vars(1);
Z = ss_vars(2);
W = ss_vars(3);
PI = 1;
Q = 1;

and where I also need:
endval; a=a_final, n=n_final; end;
Such that I feed a smoothed fitted series of values for a and n to Dynare using the shocks; block.
Has anyone got advice on this or an example mod file? Thanks.