Correcting coding / classing errors

My experience with accounting for grants required following GAAP accrual-basis accounting, which it sounds like you are trying to do moving payroll entries to prior month but seems maybe you have been mis-directed.

You should not be changing dates on transactions to be incorrect. I suggest don't follow those bad practices. Entries to "Cash" account (QB may call it 'Bank'), since those entries must match dates on bank statements.

Labor cost and payroll taxes incurred in Oct s/b expensed in Oct and billed to customer or grant for October.

Cash paid for October payroll is usually paid in November and billing for October is usually first week in Nov.

As you stated, you are not paying cash for payroll on 10/31, you are paying cash on 11/7. However, you are incurring labor expense to be billed for Oct but that also does not happen until Nov to be done correctly, right?

So the debit entries for labor and payroll tax expense in Oct. are credits to accrual accounts in October then in November, you make entries to relieve accrued payroll and payroll tax liabilities and credit Cash account.

Yes, paychecks should never be "changed" once sent out to employees or anyone else. If corrections are needed, they should be made the proper way depending on what kind of transactions need to be corrected.