I agree with all of this. My fuel only estimate cost came out around £500 too.
To give the opposite side of your view, I'd prefer to drive it!
I love listening to podcasts and audio books, so would listen to those along the way. I am, however, a confident driver with over 25 years of experience behind me.
Other things to consider. It's not just fuel costs - it's wear and tear on your car. 180 miles a day, 4 days a week for, say, 9 months is around 28,000 miles. Estimated tyre usage is between 20,000 and 40,000 miles (though I've recently gotten much more out of some of mine). How quickly your car goes through tyres depends on driving style and the car itself.
DH hasn't changed his driving style, but his old car's tyres were rubbish and he'd only get about 10,000 miles out of them. He bought his current car new and has done 30,000 miles out of them with a change only due to a puncture.
Look up how much tyres are and whether your car has a proper spare or a space saver. My car is a BMW and doesn't have a spare at all, so the run flat tyres I have are £160 each. DH's old car was over £200 a tyre.
As another idea, could you stay up there a couple of nights?
I like the coach idea too, though they'll probably be slower than the train, depending on the route.