you could try to wrap a thin strip of tape around the plug, so that the microphone pin (of the socket) does not get grounded when you insert the cable into the socket.
wrap a thin strip of tape to cover either the second ring contact area (mic/ground) or the sleeve contact area (ground/mic). one of the two should solve your problem.
yes, i know your headphones only have the Tip-Ring-Sleeve, but your jack is expecting Tip-Ring-Ring-Sleeve, so the jack has two connectors where your headphones only have the Sleeve. one of those connectors in the jack has to be stopped from making contact.