Barkeepers Friend, which is mostly oxalic acid, works quite well, with very little damage to the wood that I've been able to notice - at least with a pair of really nasty, battered, and rust stained 1950ies beechwood .22 stocks. Mixing a paste and letting it dry and brushing it off works pretty well on very dark spots. On these stocks I ended up wetting them many times, washing with oxalic acid - and the many wettings raised more of the dents up than I was able to do with the hot iron and damp rag trick. The more you do it, the better it will get. A really stubborn spot can be removed by making a wet paste, and brushing off dry. The same spot, treated again, allowed to dry and washed off with water will usually allow the stains to be visible again. So let it dry, then brush off. Give it a try.