I guess it all depends on where it was used. When I did the cam belt, by mileage instead of years, after 20+, the cam sprocket cam off by hand. It slid easily, as did the damper/pulley. No puller required for either. CA & GA ambient and lack of salted roads, I guess.
I would use a pry bar against the front of the block, not against the aluminum bottom piece. One with a 'curl' at the end that could rock or roll on the curve of the curl would work nicely. In a pinch, a crowbar(small) or Stanley flat tool and a pivot could do the job. Mix ATF & Acetone 50:50, and drip/drool that onto the crank so it can seep into the gap between the sprocket & crankshaft. Supposed to be a good penetrating oil.
Patience. and if you get in a hurry, refer back to the patience exhortation. It will come apart, just give it some time.
tom
added: Have you thought about unbolting the aluminum adapter from the block, and moving it along with the crankshaft? That would allow the sprocket to stay in place.