You need to have the Check Expense including your fees as payable to the Property Management Firm, because they are acting as your Agent and means the activity is your Vendor Name. The costs are not related to the Tenant, but the Supplier of the goods and services = your manager.
You do this with a Clearing Bank account. Treat the revenue stream as Gross Rent deposit to that Clearing Bank. Use the Clearing Bank to Write Check and Pay the property manager listing their fees and your costs here. Now the Clearing bank has your Net. The real deposit to operating bank is "transfer" from Clearing Bank. Now Clearing Bank = $0, if you did this correctly.
Here's a mistake: "...but then the property manager includes the owner-paid amount in the property management P&L"
Anything this Property Manager is doing for other people's property is not supposed to hit their own P&L. The Rent is a Liability for the Property Management firm; any Costs paid for on those properties is Advance Costs as Other Current Asset, to be "repaid" from the owners either as New funds or by reducing the Collected Rent that is sent to the owner. The Amount sent to the owner would be:
Gross Rent, reducing the liability
Negative holdback for amounts owed to the Property manager
= Net Payout
And the Other Current Asset advanced costs for Plumbing repairs, etc, are invoices, which clears the Other Current Asset account. The only Income item here is the Management Fee. The only Expense incurred by the property manager is what they contract to cover under the terms of their Management Fee, such as "We pay for all yard care, snow removal, and parking lot striping."
"which then also gets entered into owner's QB when net rent check arrives to owner, how do you fix the entries in QB so the line item doesn't appear to be DOUBLE when running a QB P&L?"
There should never be double-anything. That is always an indication something either is entered twice, or is in the wrong place. Example: Using the credit card means the Credit Card Charge Expense details are already entered; the payment against the card is against that CC type of account in QB and never lists the spending details, here, because that would be Twice the office supplies.