Here is a good solution, at least until developers of the GGIII solve the true problem.
I play a lot this game, many hours.
I started to see that saving a game or loading a saved games take many minutes. As game goes on, it takes more and more minutes saving or loading a game. As much I play the game each time saving maps or loading then takes more time. So I had to finish the game since it is no nice waiting for 5 or more minutes just to save or loading one map.
It happens many times each time I play a new game.
But then I started to see that the problem does not happen at the beginning of a game but after some turns were going. Like 40 or 50 or 70 or 100.
Then I made some test looking the turns issues and finally found the problem.
The problem is this:
When you start a new game, usually you save the map to load the map later to see if you get planets bonus (like ideology more points or research extra capacities etc) or to make changes in the decisions you make. That is ok, but the game only allows you to do that like 15 times maybe less or may be more.
But after you save and load the map more than 15 or 20 or 25 times, the game gets a bug. And that bug makes (after it appears) that saving a game or loading a game takes a little more time. But the time taking increase exponentially. I mean each additional turn you make in the game, the more time it takes to save or to load a map. The more turns you execute once the bug appeared the more times it will take to saving or loading a game. After some 10 or 20 turns you cannot play the game because not only it takes a lot of time to save a game or to load a game but each turn takes forever.
After I found the problem I have played many times this game and no more saving or loading problems. Still it takes long turn in huge galaxies but they are normal since huge galaxies take many decisions (this game still need to be more improved). But no more saving or loading problems.
Saving a game takes little time the same for loading games.
How to solve the problem?
When you start a game, try no to save and load so many times. remember that you can only do it like 20 times. A little less or little more.
If you want save or load a game more times, you need to do as follow:
1. Save the game.
2. Exit the game.
3. Restart the game. (I am not sure if just going to the main menu before loading the games works too).
4. Load the game.
In you exit the game and load the game, the bug does not appear. I have noted that doing that give you more saving and loading chances.
If you load a game that you see takes time longer to save or to load. Exit the game and get a saved game that has not the bug problem. The game will work fine if the bug has not appeared.
Developers of this game should solve this bug, since it makes a very good game unplayable.
Tell me if this help.