How do engineering or Time & Material project billing firms handle overtime processing and billing of time entry? What are they doing to process billing in an efficient way?

Here is our issue:

If OT needs to go to a different account, then payroll is required.

However, payroll uses a different processing date than the time entry items. 

Our client must have payroll in order to break out OT separately from time entry.  That seems fine, except the date of the payroll entries go over as the check date.

For example, the time cards are posted to project as 3-16-3/31, but the check is dated 4/1.  This then reverses the regular time and post it again but the payroll entries have the new date. Which causes a couple problems with Billing the entries. Also, it creates a LOT of lines in the project side and using allocation it creates many more lines in the bill, which even if we try to group due to the dates issue doesn’t come out cleanly.

The highlighted is the description but not the date on the transaction, which creates extra issues when billing.