Completely agree with splitting out the "self" and "context" actions, and also with dslyecxi's "Use" key. With the flexibility of the Arma control options, the ideas of key presses and holds can be expanded to almost any of the controls. For example, get the Ammo Selection options out of the Action menu and apply them to the Reload key. If I press reload, then reload my weapon with a mag of my current ammo. If I hold reload, show me a radial menu of my ammo options and let me choose which to reload with a quick twitch/click of the mouse.
In my opinion, radial menus are a severely under-utilized UI element. With a mouse and some good icon design, they're both easier to read and faster to interact with than a list/menu. I think they would be a huge addition to the Arma interface. Another great application of this would be dslyecxi's vehicle entrance. Tap my Action key, and put me in the nearest seat. Hold it, and show me a radial menu of seats I can access from my position. Dslyecxi suggested a scrollable list, but that takes us right back to the same clumsy list interaction that we have now. Scrollable lists are for pause menus and controllers. When you're trying to avoid fire, you can't be reading list items and hoping you don't scroll one notch too far on that wheel.
All that said, huge Up-vote for revamping context-sensitive actions in Arma. I don't even want to call it "fixing the Action menu" because the Action menu should be gone!