Roland Johansen
Deity
How do you feel about those restrictions? Are they enough to keep it UG? Technically you'd need to move a worker to the tile to figure out the partially completed builds, and you wouldn't be able to determine the improvement builds in neutral lands, but I'm hoping that's minor enough of a leak to ignore.
A player can use 'SHIFT-move-order-hover-over-build-order' with a worker to find out how long the build order would take. Removing the move order and releasing SHIFT would keep your worker where it is and you got the information for free. (I have done this before to know how many workers I want to move to a far away job.)
So the only thing you need for this information is a worker which is something that you generally have. Before you have any workers, you generally don't have any improvements partially finished. Maybe this will make you feel better of the level of UG-ness of this addition.
BTW, I have been using signs on the map to denote the number of turns until completion of tile improvements for a long time now. So this will really help me with some micromanagement. Thank you for the addition.

A question though: You added some code that stops workers chopping a forest and that signifies the number of turns left to complete an improvement. Does this code take into account the fact that workers can get different worker speeds throughout the game? For instance, the invention of steam power, the use of the serfdom civic and the construction and obsoletion of the Hagia Sofia wonder all change the worker speed and thus the amount of work left to finish an improvement. Also the game speed affects the amount of work needed to complete an improvement but is of course constant during a game. Is all of this taken into account? Will signs dynamically change when worker speed change, even during a turn when you capture the Hagia Sofia or steal the Steam Power technology?
Note that I do not question your programming skills, I just thought it might be tough to get all of that working without any hiccups.
