RE: Now, here is the problem:
I get the warning "Your Payroll is Late. Do you want to pay all by check?" when I click "Continue".
Then I get a second warning when I try to send the direct deposits (my workers have a mix, some with DD, some paid by check), again telling me that my payroll is late.

Yes, this is because you need to complete your payroll and send the DD orders two banking days before the payroll date. Otherwise the employees will not get their money by the payroll date, because it takes two days to deliver the money. Creating DD orders that won't arrive in employee accounts by the payroll date that is non-compliant, a form of "holding" payroll - something you don't want to do.

A better practice is to pay about week in arrears, a week after the pay period end date. For example, if your pay period ends on Friday, Saturday, or Sunday, make your payroll date the following Friday. Then complete the payroll and send the DD orders by Wednesday  5pm PT - the cutoff point for a Friday payroll.