Those really hard axes will ruin a file for sure. The traditional sand stone grinding wheels are just the ticket for those heads.I like, prefer, and use files/stones most often. However, I have a few heads right now (Craftsman boy's axe, and a no-name of unknown quality) that I simply cant file no matter which ones I use. The heads are just too hard and I can't get the file to bite unfortunately. My files are vintage us Nicholsons and a big Heller that's never really let me down until now. It may getting dull unfortunatley. I managed to file the Craftsman initially, but only to get an "okay" profile on it more suited to splitting. It has a really nice high centerline, so to really get it to be a nice thin chopper, I think I'm going to need to grab the angle grinder and 36-grit flap disk to thin it out. I won't be near the edge and will keep it cool with water and a rag. (Full disclosure, I have blued a thin wire edge on an axe a while back with the flap disk when I wasn't being careful). I didn't ruin the temper of the edge itself, but it can happen for sure.
I've even tried stones...the Lansk Heavy Duty and the Baryonyx American Mutt coarse stones. They work, but slowly. It would takes hours and hours to get to where I want the head with the stones alone. My last resort is now the angle grinder int he interest of effort required. The axe should hold an excellent edge though based on this!
I have a big wavy Heller that was just a rocking good file but mine is starting to go also. Just don't come across them everyday. Much sadness....