I like suggestions 1, 2, and 3.
Suggestion 4 sounds a little impractical, as we actually have 3 military production buildings, so adding all these to the menu bar would just be unnecessary clutter. Depending on your style of game play you may not even access them frequently (same for magic academy). Perhaps if instead we had a single button that opened up a window with shortcuts to all production buildings, i.e. barracks, academy, workshops, factories, etc. There could also be options like "start a bread production at all idle workshops", or "start making warrior masks at all idle steel factories", etc. This would result in only one new icon on the menu bar, so no clutter, but would add the ease you're after regardless of your style of game-play, and drastically reduce the amount of time spent on scrolling around your own city.