Ask the supplier for the loaded tool through entry and exit, using your actual machine door positions; I'd hold the purchase decision until they can show that.
Send measurements from the installed machine, particularly anything changed since the brochure; our machine had acquired a guard bracket nobody had put on the layout.
Does the tool drawing include the blank after gripping? Its withdrawal orientation may occupy different space from the blank still sitting in the fixture.
A simple dummy of the loaded tool can help everyone see the tight spots at the review. It won't replace the supplier's route check, but it makes omissions obvious.