Yep, that is life with a Grey. No telling what they or going to like or when they will like it.
I know of no way to get him in and out of the cage - today, with no training, without upsetting him.
You do need to work on either step-up or letting him come out on his own.
Then, having a way to get him back to the cage. Mine are trained to go back on command. I love it!
If Irwin is hand shy, you might use your arm, my Grey prefers it most of the time.
Good luck.