Hi Pip,
I think that posted logfile is misleading. I experience the issue as well, allthough I haven't found it that annoying.
From one of my own games:
[2014-Jul-02 21:47:31] Processing turn 384 ...
[2014-Jul-02 21:47:31] Processing AI (pre-pass) ...
[2014-Jul-02 21:47:31] ResearchAgent::process Bugs: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Giants: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Flyers: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Leviathans: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Aspidochs: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Sharks: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Invaders: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process QueenFlyers: 0 ms
[2014-Jul-02 21:47:31] ResearchAgent::process Scientific: 9 ms
[2014-Jul-02 21:47:32] ResearchAgent::process Economic: 16 ms
[2014-Jul-02 21:47:32] AI (pre-pass) processed.
invasion remaining turns: 0
[2014-Jul-02 21:47:33] Processing AI (post-pass) ...
[2014-Jul-02 21:47:33] AI (post-pass) processed.
[2014-Jul-02 21:47:33] Turn 384 processed.
[2014-Jul-02 21:47:33] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: UnitProductionComplete.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: CityGrown.
[2014-Jul-02 21:47:34] Event: BuildingProductionComplete.
[2014-Jul-02 21:47:54] Event: EnemyDetected.
[2014-Jul-02 21:47:55] Saving game ...
[2014-Jul-02 21:47:55] Game saved (465 kB).
You might conclude the turn processing took only 2 seconds, but it is only when the "Game saved" message is printed that the next round start and you can continue playing. As you can see there is 22 seconds between the "turn 384 processed" message and the "Game saved" message. I believe it is this 22 seconds that annoys people. Disk activity or memory pressure can be ruled out as a cause... my system has 8GB of memory, about 5GB unused. CPU is an i5-3210M CPU @ 2.50GHz, should be more than plenty, if you think this is still too low I'll redo the experiment on my desktop monster with 32GB RAM and a Xeon E5-2670 CPU

. No disk activity observed.
While running the game in a window, I have run a "perf top" during this 22 second period and created a screenshot:

- pandora_perf.jpg (249.15 KiB) Viewed 5892 times
Highest cpu consumer is a memcpy routine, then an unnamed function in the Nvidia OpenGL library. 3rd is a function called matchesUnit in the Pandora binary itself.
Looking at these percentages, perhaps that matchesUnit can be looked at, but I don't think there is a big issue with game code being inefficient. My impression is that the game is waiting on something... like data to come in or so. But here I can only speculate as I have no knowledge about the game internals.
If you want to have the savegame file, let me know.