OK. It seems that you have removed the screw and that you have the puller installed correctly, but the bugger still wont come off.

And tapping it gently hasn't worked. The next step is to get serious with it. As I said earlier, get yourself a two pound hammer and give it a sharp whack downwards right on the screw of the puller. Then tighten the screw a little more and repeat the process. Don't be gentle with it. If is is set up correctly you shouldn't break anything.

I know that you have checked that the arms of the puller are under the handle and that the screw is pushing directly on the faucet spindle and is not itself overlapping the screw and pushing on the handle.

If the puller screw is too large in diameter that can sometimes happen.

If all else fails you will have to cut the handle off with a hacksaw, being careful not to damage the spindle. Replacement handles are cheap.