Forster Seater dies have a sliding sleeve that is reamed to slightly larger dimensions than a resized case, similar to the actual chamber in the rifle. This is why they are sought after for loading straight ammo, but unfortunately means the seater for the standard case will not work for the AI as the sleeve will not fit over the blown out case. The Hornady seater dies have a floating sleeve that only contacts the neck of the case, so they are not cartridge specific, only caliber specific. This makes them great for AI cartridges because the seaters for the standard cartridges do work for the improved variants. Same goes for the Lee collet neck sizers. They only contact the neck, and the "shoulder" inside the collet is 45*, so no issue with the 40* AI shoulder.
Sizing the body of the case is the only thing that requires a cartridge specific die. For my improved 6.5x55, I use a Lee Collet for 6.5x55, a Hornady seater for 6.5x55, and a custom Whidden body die that was based on three pieces of twice fired brass I sent them. On the improved cases, you can get by just neck sizing for at least the first four firings on the brass normally because the design limits brass movement, maybe more with less than max loads. Because of this you can still shoot the gun for quite awhile while waiting for the custom die that you will eventually need. Mine took 10 weeks to get a couple years ago, probably be longer now. Let me know if you have any other questions.