If I understand you right, we're talking about the same thing. Cutting the wire and adding an extension in between isn't a fix, it's a workaround.
Anyhow, you were asking for the connector, not the wire. As I said, you already have the connector. What you need is the hollow pins for new, longer wires. Or longer wires with the hollow pins attached. Then you just slide the old pins out and new pins in into the connector. Also, the flat strip of wires looks exactly like the front panel wires in some computer cases. Not only USB as I suggested in my previous posts, also the front panel audio uses that size of pins and their cables are usually longer. The front panel LEDs and switches apply, too. I have a bunch of them salvaged, but the mailing costs would be ridiculously high. Go check your local computer builder shop for some last millennium stuff you could get for next to free.