@Soh Tanaka Quickbooks has issues in tracking transactions by class especially for bank accounts, that's why it's not recommended to use the details of Funds Held by PM account when you review transactions by class. The only way you can get an accurate report by class if when you book everything using a journal entry which is not advisable either.
Owner distribution from PM should be recorded as a check/expenses in the Funds Held by PM register payable to your name or LLC name, categorized as Undeposited Funds (then process bank deposit) or directly categorized to Checking account (where the fund is deposited to). It depends on whatever you trying to accomplish, but if your books and process are set up properly, you should be able to run report that will show you the info you're looking for.
As far as the different ways to process the revenue, creating an invoice and processing a payment will track (show in the customer transaction details) which customer paid and who hasn't and when you run P&L report in accrual, income will be recognized at the date of the invoice, cash basis recognized at the date of payment. Sales receipt will track (show in the customer transaction details)customer who paid but not those who don't, P&L report using accrual and cash basis will show the same result. Bank register deposit method will not show transaction in the customer transaction details, P&L report using accrual & cash will show the same result. I highly recommend the invoice method.
But as Natalie said, this kind of issue is better discussed live with the professional that can review your set up and accounting process and at the same time help you navigate through the reports available that will show you the information you need. Good luck!