For this, you keep setting up more of the Same payroll item type, payable to different Vendor Names: "but the support team could not find a way to set up multiple entries for S-Corp Medical because we pay 3 separate companies"
This part is your own Pay Liability process, not controlled or controlling the payroll item: "(some out of checking and some with credit cards) for health, dental and vision policies. How can I set these up so that the payroll liabilities correctly post to each different payment account?"
They don't post to the Payment Account. A Person will initiate the Pay Liabilities, when you are ready to make the payment. The Tax and other Liabilities are in the Liability account, and they are there by Payroll Item. Examples:
Select to Pay Dental, to that vendor name, from Checking.
Select to pay Health, and on the Liability check being created, click on the Expenses tab and enter the same total here as Negative and post to your credit card Type of account in QB. Hit Recalculate; you just shows the Payroll system you paid the specific Payroll liability Item and amount for that Period, the Check is a $0, and the Amount just transferred to your CC account balance in this QB File.
You don't need a tax table, to use your own Calculating items with the file set to Manual Payroll. You won't see the Pay Liabilities screen listing what needs to be paid. You need to use Create Custom Liability Payments, in this case.