Ok cool, PB's post confirmed that my thinking was right, and I was going to give a rather detailed explanation, but this makes it much easier.
Can you test the DT770s on your Crack? Mine work fine there, and the headphone jack looks exactly the same.
You may be able to bend the top (as in the picture on my link) switch to get it to disconnect with the headphones plugged in, but you will need to ensure that it engages again when the headphone is plugged out. Really odd problem though. I use a right angle connector on my headphone jack. Headphones plug straight into it. That may also solve your problem.