250 Strange noise/vibration when driving hard?

I've had a 250 cup for a few months now and love it to bits. Done loads to it to get it properly sorted but there is one thing that I can't figure out.

A few weeks ago I went for a very spirited drive with a mate and then another today. On both occasions i noticed that after a prolonged period of fast, hard driving, maybe 10 mins or so, I get a noise/vibration from underneath the car in the area of the gearbox.

It happens as I come off the throttle from high rpm but goes again as soon as I accelerate. This only happens after I've been giving it the beans for sometime and does not happen at all in normal day to day driving even when hitting the rev limiter in 3rd/4th etc. It's as if something is getting hot and expanding and then catching/rubbing on something! If left to cool down a little the noise goes away for a period of time. The gearbox itself appears perfectly fine with no issues to speak of.

I have noticed that when coming on and off the throttle, particularly in 3rd, the gearstick moves forwards and backwards a little. I have just fitted a Vibra Technics lower mount in a hope to stop this but it hasn't. The other mounts look fine, but I have checked the one on top of the gearbox yet.
Could that movement be the cause of the noise? If so, I don't understand why it would not make the noise all of the time regardless of the conditions.

The only other thing I can think of is that it does have a Miltek cat-back. Is it possible that isn't lined up particularly well and is creating the noise when very hot? No idea really, just a thought.
Any ideas? Thanks.

 

Thanks, but surely with this type of defect, it would do it consistently, not sporadically when driven hard?

 

Ah, I see what you mean. Should there me any stick movement when coming on and off the throttle? I can't remember if my 265 did it or not. Its not massive but mostly noticeable in 3rd.