Keep the same generated four-bar. Rebuild the longer fingers and pads in their original local motion frames, preserving the existing shank sections and 50 mm exposed reach. Model the mating UR5e flange from its official drawing, including the male pilot and locating-pin feature. Recalculate the BOM from the parts and check finger bending separately from planar drive torque.

Official drawing: https://www.universal-robots.com/developer/hardware-and-motion/mounting-installation-robot-arm/
The robot-side flange has four M6 holes on a 50 mm PCD at 45, 135, 225 and 315 degrees, a central 31.50 mm H7 female recess, and a 6 mm H7 locating hole at 12 o'clock on the 50 mm PCD. Use a mating male pilot and a radial locating slot on the gripper side. M6 screw penetration into the robot must not exceed 8 mm.