Earlier quoted context omitted.
The answer to your question is GPS devices. They're supposed to take into account (most of) what you mentioned, and even though consumer GPS devices are fairly cheap and not up to industrial or even military GPS, time is one thing they do right. In fact, for several projects that needed a reliable time source instead of using the (as you noticed) poorly implemented atomic clock radio frequencies, we would just buy GP…
NTP does a lot more than what you theorized about and none of it is trivial. FYI: Ping is a remarkably bad tool to gauge the accuracy of remote time source. What is the delay value from "ntpq -p" I highly doubt that Apple's time servers are your best bet for time synch. Use the pool.ntp.org servers, preferabbly with your country code: e.g. us.pool.ntp.org, ca.pool.ntp.org.
My ntpq -p output:
remote refid st t when poll reach delay offset jitter
==============================================================================
time.apple.com .INIT. 16 u - 512 0 0.000 0.000 0.000