Hunter,
I'll jump in on this to try to get the conversation started for you. There are some other threads in 401k Topics on this type of situation, so dig in and research what you can.
I don't like entry defined as payroll period. It becomes messy. I prefer to say the employee becomes eligible 10/1 and each paycheck after 10/1 would have deferrals withheld.
I think of this topic with this logic. When does the employee become a participant and when do they get paid. I don't normally chase the pay periods, because the pay periods get me to the questions you are asking. I want the w-2 as my best friend, so whatever is on the w-2 for deferrals is the total I want to use for the testing. Otherwise, I may be removing a payroll from the beginning of the year and adding a payroll at the end of the year. (or vice versa) I find this to be inefficient.
How is the plan handling newly eligible and timing now? I think you would want to stay consistent.
But to answer your direct question as you stated it. First date of entry payroll period was 10/27. The first date of check for this payroll period was 11/15. I would have payroll start withholding for the 11/15 paycheck.
Others may have a different opinion and that's cool. I would just try to stay consistent in the process.