I ordered a new spider in the hope that it might help in the shifting department. (From old-style down to compact). I probably could have bought a whole crank for the price of this spider !
My next dilemma was how to get the spider off the crank. Its screwed on via male threads on the crank arm.
The answer to the predicament was quite logical.
1. Remove the small anchor bolt at the bottom of the spider.
2. Loosely attach the crank to the compatible bottom bracket of a fixed-gear bike.
3. Pedal backwards slowly, with force, until you feel the crank arm move independently of the spider/sprocket/chain/wheel. Gently continue using the crank pressure, or remove and continue doing it with your hands.
4. Pre-heating the crank with a hair dryer may help to loosen it.
Anyway, it was a great success. Now I change my spiders as I need too.