Some good points made by Dan above.
Whilst only having experience with a Moto Guzzi final drive bevel box, I found it relatively easy to shim up. Being the UK parts distributor and having the full range of shims in stock helped of course

I started with a new crownwheel and pinion which were always factory supplied as a matched pair, in this case a higher geared set from a V7 Sport. Pinion tooth engagement was adjusted first with shims to ensure its teeth spanned the full depth of those on the crownwheel. Engineers blue was then applied to the pinion teeth and the box assembled complete with gaskets, and various crownwheel shims tried until a centrally placed contact patch was found on the latters teeth following turning of the pinion shaft by hand.
I see no reason why the crownwheel and pinion engagement of the Quaife box couldn't be checked in a similar manner, although I accept that access to the full range of shims may be an issue.