Me and 3 other friends are also getting the same problem, in several games. This "Waiting For Players" spinning globe hang happens at seemingly random points in our games (turn 40, 137 etc.), leaving us unable to select any units and reloading the save, for a while, allows us to progress a few turns, the turns decreasing between each save until it no longer changes when the hang happens.
We tried a game between 3 of us as well, still getting the same hang.
We then disabled all our DLC and began a new game, but we still got the hang.
We each tried hosting the savegame, but the hang continues to reoccur.
We tried hosting the game whilst we all used DX9, still the same hang.
Then we tried deleting all our units on the turn before the hang happens and this fixed the problem for several turns (being able to change production and research etc.), until one of us tried buying a scout, which we did, and the hang reoccurred when we Next Turn'd. So we can say that the problem involves the presence of units, although we cannot figure out what initiates the hang in the first place.
I should mention we do not experience the "5s, 10s, 15s" issue that some people have, although we have in the past and solved this by reinstalling our NICs in the Device Manager, and if the problem does reoccur, we host from a different person and the 5s, 10s, problem is reduced to a mediocre ping between two people, around 250ms.
Another detail: if any one of us disconnects, the turn then finishes, even with units still on the screen. The person is then re-invited at the beginning of the next turn and this produces continual excessive lag for all players, and the hang repeats next turn.
Does anyone have a suggestion for what to try next, and is there any more details I should mention?
I have attached a save file which includes a game between 3 of us, and the broken turn is between 136-137.