I don't care as much about redesigning the menu as I do about extracting certain items from it.
The action menu should be something we use tactically instead of in the heat of battle. I think removing the weapon switching from the action menu is essential for this.
Also, contextual actions are currently too unpredictable. It is nearly impossible to guess which action will popup or the precise way you need to stand to get the action to display. a dedicated context button and improved line-of-sight context detection would be all we need to fix the main issues I have with the current setup.
At the very least, disable actions for objects that are behind me or behind a wall/door.