I use the standard Shimano or Campagnolo external cup bottom bracket tool for this, which works with both ITA and BSC thread versions.
I believe Park BBT 69.2 is correct.
![Campagniolo Tool](
![Shimano Tool](
![Park Tool BBT 69.2](
Perhaps your tool is damaged if you're having problems. Or maybe your tool is the newer, smaller shimano type for the itty bitty newer Shimano bearing cups.