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...I never attempt to pull a crank arm on a square taper crank without liberal use of some sort of penetrating oil applied both at the interior and exterior surfaces where the crank interfaces with the spindle. But I also have a puller without a handle, and the advice about getting one so you can use a longer wrench is good advice.

I detest those Park pullers with the integral handle. Not only do you lose leverage, but you can't put the lever arm exactly where you want it, like you can with a hex wrench. If you take your puller to a specialty fastener place, you can usually find a hex head bolt that is the correct threading and length (similar to the bolt now welded to the handle). You need to neck the business end down a little for cranks that attach with a bolt rather than a nut like yours. With your crank, a buck fitty bolt, and a wrench to turn it, you should be in bidness,