Well these are just some ideas I have. Nothing more nothing less.
Why not simply do things in pseudo real-time?
Bascially, time passes in ticks. A turn passes in say 2-15 minutes, which is agreed upon by the players when creating the game at the begining. Or as a default setting you could limit the time of ticks by the galaxy map size everyone chose to play on. A few minutes for smaller maps, up to 15 minutes for really large ones.
This way you can start your research for example, knowing that turns will tick on and techs will be discovered as time passes, then you can just pick the next one.
With time ticking by, say you've got 5 turns to go to get Trade and you agreed to have a time factor of 5 minutes=a turn? Well then, during that 25 minutes you can play around with the ship designer, any number of colonies, several diplomatic meetings, move several ships there full allotment of movement, etc.
What about early game? When it wouldn't take 5 minutes to do a turn? Yes that could be a problem.
Perhaps in the early game, turns will tick by at an accelerated rate. So, provide an option when the players are creating the game for accelerated turns, time ticks by in only 1-2 minutes for the first 20 turns or so.
Going further with this you could provide an in game option to accelerate the game by asking all players to vote on decreasing or increasing the passage of time. If the players agree to discuss it the game pauses while they determine the new time quantinty of each tick.
Everyone would have to agree on this, hopefully preventing allied players from monopolizing the passage of time for their needs. If no one can agree nothing changes and you can't ask for a vote on this again for the next 20 (or perhaps more) turns let's say. I think of it like the UFP meetings, where you must vote on something or nothing happens, so if you vote "no" then the vote is over and can't come up again for 20 turns. If something happens here though and the last person doesn't vote, what then? Well then I think everyone should be able to cancel the vote, and again this causes the option to be unavailable for a set amount of turns. At this point I would expect the other players that didn't like the outcome would perhaps handle the "no-voter" by their own desires, heh heh.
Dimplomacy: In a 2 player game with any number of AI, just pause the game during the diplomacy screen when it is between the human players.
You don't really need to take long during diplomacy with the AI players either, so those could remain real-time.
If you took say 5 minutes (and your game turn ticks are set to 5 minutes) in diplomacy with an AI race well perhaps you really did spend a whole game week hammering out that deal with the AI.
With multiple human players (more than 2), dimplomacy could be done real-time. This would give any other human players a chance to do something to disrupt the negotiations also, a whole new aspect could be added to the game by this.
Ship combat: In a 2 player game, you could pause the game again when it is between the 2 human player fleets.
Against the AI and when there are multiple players I think it would be better to prevent the tactical simulator from automatically coming up, but allowing it to record a demo of the battle that could be watched at some other time if you so chose (maybe during a long turn that you don't need to do anything). Perhaps you could even pass the demo on to other players in the dimplomacy screen, maybe to show your fleet superiority to them as bargaining leverage, or share the tactical demo with someone so they can see what they might be up against.