Keep the DS3231; it's very accurate.  One of my clocks uses it, and it has 
drifted about 10 seconds since daylight savings started more than 6 months 
ago. My wristwatch demo board has been running 1.5 years and it's also 
within a few seconds. If you want anything better, you'll probably need GPS 
or a rubiduim time standard.

I got a few laughs from a $1 Chinese RTC board; wickedly inaccurate. I just 
swapped the DS3231 with a genuine Maxim device and use that in my clock.

I recall most crystals are accurate to around 10ppm, which is about 1 
second per day. My interpretation of that is the manufacturing tolerances 
result in multiple batches of crystals that will fall within 10ppm of their 
rated frequency; I suppose you can pay more for cherry-picked units that 
are more accurate.  I doubt individual crystals drift back-n-forth, so you 
could add some offset to your software and fine-tune it to each crystal if 
you dont want to use RTC/GPS/Internet time.

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