I have the same problem, aka turn 200 - 357 wait hang.  I have windows 10tp build 9926 the latest AMD Radion R9 270 drivers, and well the latest of every thing.  8gb ram, FX8150 overclocked to 4.7ghz (stable for 2 years *Woot!!*) 90gb SSD, 1TB HD, Also I have the 0.71 opt in hotfix for GC3.  Tried having the ai play for me trick, truning off each one, one at a time, of the graphics options, and sound, Nothing.  Still hangs I have noticed these issues, when loading my save from before the hang I hear an odd sound from the game no matter what audio out put selected.   I tried submitting a help ticket earlier but my PC crashed.  I had 800MB of crash reports to send you but I deleted them to try that as well as saving space. Also I wanted to point out how much ram GC3 uses I have, according to the victory have 50% of the Tech researched about 50% of the map explored, also I am using an imminence galaxy with all races available and me playing Alterain. My task manager tells me when in game and before the hang I was using 90% of total ram my pc idles around 17 - 20% on most desktop tasks.