When you say ESID locking differential are you referring to the QDII Electronic Limited Slip differential? If so unless you had the 3.55 gears installed in that differential I'm almost 110% positive they all came with 3.73 gears. The only vehicle that came with 3.55 gears is the QT II V6 which are rare.

Also why are you selling all this? I thought you were going to do the gear swap and had everthing set to convert your XK to 4low?