Using fiduacial data Solenoid is 208.954 mm (8.22655 inches) in length.
Distance to center from outside entrance end plate is 104.477 mm.  
104.477 mm from entrance end plate wil be defined as z=0.

Center of end plates = +/- 99.477 mm

Distance from entrance endplate to plane of cathode is 3.6135" = 91.783 mm.

Cathode distance from solenoid center = -104.477 + -91.783 = -196.26 mm

Coil Measurements use a left handed coordinate system.

Height to middle of coil from table 142.74 m + 50.77 + 55.50/2 = 221.26

Hall Probe thickness = 2.02 mm.  Distance from front of hall to element = 2.02 - 0.9 = 1.12 mm