In QB, you avoid JE for anything to do with Names, for AP, AR, for Sales, for Sales taxes, for QB Inventory, and for QB Payroll.

There is Nothing about a JE that cannot entered using the proper transaction type.

You stated AP. But AR is not Income. It's typically accrued Expense: "One of these entries was a debit to A/P and a credit to income. The goal was to record 2018 income that was not posted until 2019."

That would be an Invoice; and if you are an accrual basis entity, that shows. If you are a cash basis entity, you switch the reporting to Cash Basis, and that won't show unless what is on the invoice hits another balance sheet account. Example: selling Inventory shows AR and Income on Cash basis reporting.

"Now this entry shows as a credit on my unpaid AP report."

A Credit to AP is posted using Enter Bill, not JE. Enter Bill, listing what is on the JE, and this will Credit AP.

"I don't know how to fix this without changing the retained earnings balance as of 12/31."

Never let someone use JE like this; when Names are involved, and especially for Income, you use Customer Transactions. For AP, you use Vendor Transactions.

I would replace the JE with the Right Transaction Type for that name and the function.