"So I deleted the JE and went back to reconcile and the payment was again not there."
Not "where"? In the first screen on the Reconciliation function? In the second screen, on the right side of the reconciliation screen, as a transaction listed? Are you limiting the date range for this view? Are you checkmarking any transactions in the Register, which is NOT something you do?
"I was looking at the Register view for payments/credits. The JE was credited to the CC account."
Any entry that hits the CC account shows in the CC register.
"Balance was correct from statement. It seems like I have to enter the payment twice for the reconcile to credit it."
Never Enter Data 2wice. As soon as you think that is what you need to do, you are making an error.
It is easy to follow the data flow:
The credit card account Register view is no different than a bank or any other balance sheet account register. Balance sheet accounts carry a running balance. Transactions that affect this account result in changes in that balance.
You use the Reconciliation tool to enter a known ending balance, then you use the function for checking as cleared any transactions in your system that you ALSO see on the statement, to confirm they processed your data correctly and that you entered your data correctly, and they don't have something you did even know about (potential fraud or error).
You end with a Difference of 0 because you and that statement agree.
"My reconcile window said I was balanced"
Did you complete that reconciliation? Once you completed it, those transactions are marked as Cleared and will not show the next time you reconcile, in the reconciliation tool.
They always exist in the Register as long as you don't delete them.