Anyone wanting to use an R31 Skyline diff would be wise to also find a crown wheel and pinion from an early 6 cylinder Cortina as the case hardening if vastly superior to that of the later Borg warner variants.
The technique for shortening Borg warner housings is to use the short tubes and axles for both sides rather than the original setup of one long and one short,this requires removing and refitting with plug welds etc the axle tube and you must use a brand new short axle,I cannot stress to much use a new axle as when used in the side other than where it was fitted stock the stress reversal will break the axle with any decent power output.
Only a new axle that has yet to see any driveline stress will last.