20 ° is way out of my limits for an HSI to be used under IFR, even if the deviation card for the HSI should show it (which I really doubt). If the deviation card is incorrect by more than 5 °, the plane must not be used for IFR, if I do remember right.
Electric de-icing might cause an additional off-set.
Putting the system in free mode is a good idea in your case and even a legal solution, if placarded at the switch ("slaving u/s, use free mode only").
But since the adjustment is normally not a big deal, the slaving should be fixed.