After comparing the outlines, I found that the proposed approach overlaps the door handle even though the workpiece itself clears. That explains the misleadingly comfortable result in my initial sketch.

Use that measured layout to review the complete approach and retreat offline. Include the tool, cables and service access, then ask the integrator to assess a revised mounting arrangement.

Our buyer says go bigger. Does that help, or just buy the same problem in a larger arm?

Going larger should open up mounting options. It might be the most straightforward option to explore.

Bigger could bring another obstruction. Extra reach won't shrink the gripper past that handle.