Year 3535
I have to admit,
@smurphys7 getting to year 5000 really took the wind out of my sails. My goal for some time has been to get to 5000, which I thought was a goal no one else was ever likely to reach. But I've recovered. Mostly.

My goal now is still 5000 (or maybe more, if my plan works), which would take forever, unless I can moderate the sine wave to the point where I no longer need to rebalance workers and laborers every 50 years or so. I'm going to try to flatten the wave to the point that I never lose all my laborers.
To do that, my plan is to shut down my extra houses, and to release them back into circulation in a very stingy way, so the pop curve climbs in a more shallow manner. I hope this will result in a flatter sine wave. We'll see.
Image 1 - I have started this program at the bottom of the wave. You can see that I have 783 houses and 600 families. I went through and closed down every house that was empty (not many of these) plus every house that had a single male. I could have selected every house with a single female just as easily. I figured this was a reasonable proxy for unnecessary houses.
Image 2 - And when I finished this, I had 615 houses. Good enough. Look at all the homeless guys.
Image 3 - By the time all the homeless folk had settled in, I was down to 611 homes and 594 families. This is my starting point. From here I'll run attended until all the houses are open again, but my plan is to let the number of families fall behind the number of houses. I expect the result to be a flatter pop curve.