Calling campagnolo experts

@Mike - bugger, forgotten about that "trick"

It goes against every instinct but, after soaking the thread, you might try tightening the cup a fraction (anti-clockwise) before attempting to loosen it once more. For reasons known only to the gods of spannerisation, this sometimes yields results.

The LBS is more than likely simply going to apply more torque than you have currently... going there is only to try and claim off their insurance if it goes wrong I guess?

My approach would be lots and lots of leverage and gentle application.

Scaffold pole would be my go-to for this.

when the only option is the application of a Birmingham spanner or excessive force it is time to get it to the LBS.

concur with the lbs option ... too much torque and you could damage the
frame

You may not want to take it to your LBS, but they should have the experience and tools to sort it out. I've had to accept defeat and do this for a stuck BB before.

Having said that, I recently managed to get a BB out with a 2 foot breaker bar and a lot of effort, but that was on a steel frame. And a bench with a vice would have been easier.

Dumb suggestion and stating the obvious but have you removed the spring clip that sits on the drive side of the bottom bracket ?

You don't need a torque wrench to take it off. Use a big open ended or adjustable spanner. Hit the end of the spanner gently with a hammer. That should budge it, unless someone's used loctite (why?)..

I am guessing here as i don't know what frame, alu cup into alu insert bonded into the carbon bb shell.

Proceed with caution, i am aware of frame inserts falling out, depends on which is stronger the corrosion or the glue.

what's the frame made of, i am assuming this is a metal frame and threaded, you are trying to undo the cup the right way??? Could try using plusgas/etc to soak into the thread and try again after a few hours. If it really is seized, be prepared to risk the frame.

drive side or non drive side?