You are right in the sense that the aerodynamics don't change. A certain RPM gives you a certain IAS, independent of the wind. However, you were doing a ground-referenced maneuver (descending along a fixed path to the threshold) and because of the headwind, your air-referenced path was more shallow than usual. And to maintain that shallower glide path you need more power.
Think of it like this. In still air, your glide path, both ground-referenced and through the air, is maybe 5 degrees (I'm assuming a VFR circuit here, and not an IFR approach). Once you get a headwind, your ground-referenced glide path is still 5 degrees (the picture outside is the same), but your glide path through the moving air is now maybe 3 degrees. The stronger the headwind, the shallower your glide path through the air. And that accounts for the difference in power setting.
In addition to this, crabbing also has a modest effect, like you suspect. Because of the crab you fly a longer distance through the air, while covering the same distance over the ground. This leads through a shallower glide through the air, and thus a higher power setting.
As far as flying technique is concerned, in a strong headwind I tend to keep up the speed on final, otherwise you'll never get there. I reduce speed to Vref much later than I would normally do, and apply full flaps a lot later than I would normally do. Because of the headwind, it turns out you've got plenty time for that anyway.