Omelette perhaps? When you wiggle the cable, I can't tell from here whether you have a broken wire inside the molded connector, or you have a contact connection problem. Hold the phone and connector in one hand so that the connector doesn't move. Then, wiggle the cable and see if it's still intermittent. That should separate the potential causes.
Also, if it's that bad, I would tear apart the phone and visually inspect the connector. Same with using a magnifier to inspect the contacts from outside the phone. Might as well run a stiff non-conductive brush through the receptacle while you're at it. Pocket lint tends to be the same dark color as the connector insulation and is difficult to see. I've seen phones that I swear looked clean when I looked inside with a magnifier, yet had an accumulation of lint at the bottom of the connector which was preventing the connector from seating properly.
So much for that idea. I've seen a few cables that are mostly insulation with very little copper. Maybe tear apart one of the cables that had previously failed.