Actual that does not look to bad, very nice so far. Just for what it is worth the part of the hat with the ridges is going to be a whole lot of fun to plannish real smooth. What you probably need to do is make a stake at the whole profile of the side of the helmet. This way it will be easier to keep true. Once you start smoothing out the ridges things will move a lot. I wood go with a wooden or rawhide hammer over the largest section to get smoothed before plannishing. Anneal for sure.
Since all you have are the HF hammers you can make those into a fairly decent hammer. If they have a wooden handle I wood remove, fiberglass leave in I guess. They are a little soft and if no handle you can super quench to face harden. Any how make yourself a couple of templates out of sheet of copper like I mentioned earlier. Now file to the correct profiles. Then sand with 150, 220, 320 then using black compound buff on a yellow buff until mirror finished. You also need to do the same to the stake. Then just hammer away and hammer, hammer, or a tap, tap tap until your are done. Note just to make thinks simple use a wooden hammer on a wooden stake and true up the best you can. If annealed it will smooth out fairly well and no hammer marks.
Now if you search somewhere on this site is a good picture of hammers. hmmmm

www Metalrecipes -- heat and beat to the desired shape, repeat as necessary.
warren