It turns out that for some unknown reason, the video driver flaked out and the PC reverted to some generic driver that is far too inferior to handle GC3 graphic requirements.  Rebooted the machine and all has been well for the last... 5 hours.

Which is peculiar.  Like you, I am playing an Insane-sized map.  Once I had uncovered about 1/5th of the map, I started to get some recurring lagging.  Not a temporary freeze, but rather the PC slowed way, way down.  Like trying to sprint through ankle-deep molasses.  That would last for about 5-10 minutes, and then I would have another 5-10 lag.  That's how the last few hundred turns have been like.  Until just now.

All things considered, I'm wondering if my NVidia 353.06 driver is the culprit.  NVidia has been trying to optimize for some newer graphic-intensive games lately, and trying to promote their Game Shield software that can also stream TV shows.  There's a whole lot of stuff in that code that could get in the way of solo-player games that do NOT include a bunch of cut scenes.

 I was just playing GC3 for about two hours with no lagging.  I checked the GeForce Experience and see that the 353.06 driver was released on 5/31, which is before I started playing GC3.  So this whole lagging thing is NOT related to my hardware because NOTHING has changed there.  Nor is it because of my video drivers because I've been using the same driver all along.  That leaves either changes that occurred at Steam or Stardock or both.  Something that was causing lagging is no longer doing so.  Definitely a Good Thing, but quite the mystery as to what it was.

When the driver failed, it popped a message letting me know it happened.  That was when I was on my desktop, playing some Solitaire.  I couldn't see any difference in the graphics, so I figured "no big deal".  But apparently it was.  Rebooting the PC not only restored the NVidia driver, giving me full functionality in GC3, it also eliminated the lagging I had been experiencing in the game ever since @Turn 100.  (Insane map)  Something has changed for the better, but I have no idea what it was. 

Thank you!  Disabling the Steam overlay seems to have remedied the problem.