I can't judge the arm choice from that, but ask both suppliers to use the same complete tool model against the installed machine geometry, including the open door
Then have the integrator define the loading sequence and review the corresponding orientations, because agreeing on a tool shape alone won't resolve a pose disagreement
Include who approves later tooling changes in that discussion, or the agreed clearance can disappear when somebody substitutes an adapter after the order
For the shared geometry, yes. But don't merge the disputed orientations into one tidy pose; attach each to its proposed loading step so the disagreement survives the drawing cleanup