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i am worried the tool is too "soft" for the plastic to turn it!
The plastic tool is fine when used correctly. The Park BBT10.2 doesn't bring anything to the party except about 400% price premium over the plastic Shimano TL-FC16 and a temptation for the incompetent to over-torque the preload screw.
If you want to go #tartmode, this works and uses a big Allen key which you already own, so it's almost as cheap as buying a new Shimano tool and a fifth of the price of the Park tool if you absolutely must go plastic-free.
It's not supposed to remove the crank, just the preload screw. It shouldn't be more than finger tight, so once you undo the pinch bolts (you have done that, haven't you?) the preload screw should come out very easily. If the preload screw is OK but the tool isn't, you can just buy a new tool for a few quid.