Long ago I asked this question on quora, it got OK answers including one of my own that's now deleted, but this post prompted me to check on it again and it's now got a really great answer, check it out: https://www.quora.com/During-the-Apollo-launches-what-happen...

In particular I am happy about the timing. They accept inertial guidance to be a bit off because transferring it closer to T=0 would make it less accurate because of rocket vibrations!