The issue appears to be that a period of time that takes more than 60 seconds to write a response results in the server mistakenly believing that the script has timed out. All settings are correct so this is an issue with the hosting server which I am attempting to get corrected with the hosting provider.
As a test you may want to write a post and wait 61 seconds and try to post, it shouldn't post after that time (if my theory is correct). If I'm wrong, I'd like to know that too.