Hi there, Billavoider.
I appreciate the detailed information you've provided. In Intuit Online Payroll, transferring your employees' payroll details, you'll have to manually enter them as Journal Entries. Moving forward, you'll have to change the information on the payroll settings with the correct bank account.
Moreover, I highly suggest consulting your accountant for guidance on which account receives the debit and credit side of the transaction. This is to ensure the accuracy of your books. You can check out this article Find an accountant.
Please let me know if you have any other concerns.