I mostly use a pocket stone or a puck to maintain the edge bevel (followed by a loaded strop if I want to use it for carving); until now I haven't had the need to use a file. I've only sharpened the bevel, and, unless I run into a major mishap that takes out a chunk of the edge, I don't forsee the need to re-grind the concave anytime soon.
If you should ever reach the point at which you would need to reprofile the concave, you have a few options:
1) Use a file or emery paper to work on the concave manually. When using emery paper, you can make a support from wood that matches the concave. With files you need to be quite proficient, but it can be done.
2) Put the concave to a grinding wheel (or a beltsander with appropriate radius) and thin it down - if you don't have the equipment, I'm sure the Spyderco sharpening service will help you out; alternatively, everybody with a grinder who knows how to use it can help you.
3) Have the edge drawn out and re-hardened/tempered by a smith, but that will surely void the warranty. Follow up with step 1) or 2).
As for the spoons; you can't carve them all the way to their final shape with an axe, not even with the HatchetHawk.
However, the bulk of the wood - I'd say easily 90% - was removed with the HatchetHawk. The closer you can work down to the final shape with the axe the less work you have to do with knife and hook knife. That's where the balance and precision of the HatchetHawk comes in - because the last thing want is to ruin your spoon blank with a missed blow when you are already close to the final dimensions.