Hit it harder
I had to hit mine *really* hard for it to move. The problem is, no matter what method you choose, it'll need to be unscrewed so you can put the new one in. Unless you want to make a new hole for the second one.
You also don't want anything to get into the tank. I had a tiny bit of insulation fall in and has made it's way to my taps in the kitchen, vastly reducing the hot water taps flow. I keep meaning to sort it but I've not got around to it yet.
If you don't want to add heat, have you considered freezing it? Go and grab some pipe freezer from Screwfix / wherever, make it as cold as possible, and then hit it.