What I call the "reduced city screen" is what you see when you just click on the name of a city in the main interface: the bottom of the city screen will appear, letting you change builds and hurry/draft mostly, without entering the city screen.
What about improving this reduced screen, like by adding something similar to what is proposed by EF here: http://forums.civfanatics.com/showthread.php?t=307951 ?
That way, you could use the governors and see the result in terms of hammers/science/... without actually having to enter the city screen.