deflection = (P*L^3)/(3*E*I)
P = load,
L= length from spindle to end of rod,
E = modulus of Elasticity,
I = moment of inertia of a round cross-section.
For an estimate of what the deflection will be for the stainless, swap out the "E" for the aluminum for the "E" stainless after you back calculate the applied load "P" since you already know the deflection for the aluminum.
Typical "E" for aluminum is 10.3e6 and 29.0e6 for steel.
If I had more time I'd do it for you but I don't right now sorry.
This will just give you an estimate as there are other variables that come into play like the changing diameter but since the "E" of the steel is approx. 3 times that of aluminum, you'll see about that much difference in deflections.