I have always adjusted front wheel bearings (new or repacked) by nipping up the nut (not wringing it's neck) and then backing it off until I had play. Then carefully tighten the nut until all the play has just gone and stake the nut there. I have done this on road race and rally cars and never had a problem. I see the factory workshop manual allows for .001 t0.004 inches (1 to 4 thou) axial play. And as you say the MOT man doesn't like any play at all. Been there, done that, lost that arguement. (NO PLAY MEANS NO PLAY)
It has always struck me as odd that the nut on the left side is right hand thread and vice versa. This means that that given the chance the nuts will undo rather that do up. As long as the washer is fitted and the nuts correctly staked it won't happen. I always prefered castleated nuts and split (cotter) pins myself. The only time I have ever seen a problem with Fiat nuts coming undone is when someone has assembled the wheel bearings without the washer and the they only come undone so far before they destroy themselves and seize.
Allan