I worked as a Mechanic in a Fiat/Lancia Main Dealership workshop in the '70's i.e. when 500's and 126's were often in for servicing etc.
We never loaded the car when checking/adjusting toe-in/out on any of the cars (fwd cars were set to toe-out). What we did was iirc set the tracking to roughly 1/2 the Fiat figures, so e.g. if Fiat stipulated 0-2 mm, we set to 1mm.
Seemed to work fine. With lots of regular customers we could track the tyre wear, never had any problems with excessive tyre wear (other than if e.g a balljoint/kingpin was worn).
Adjusting the 2 track rods so that they are the same length is very important - if they don't match, they need to be equalised first, then the tracking checked/set. Otherwise the 'Toe-Out-on-Turns' will be wrong leading to excessive tyre wear and weird handling/cornering issues. Toe out on turns means that the inner wheel when turning e.g. the left wheel when turning left) turns through a greater angle.
If your steering wheel is misaligned when travelling straight, 1st equalise the length of the track rods, then set the tracking, then remove and re-position the steering wheel so that the angle of the 2 wheel spokes are equal relative to horizontal.
To remove the steering wheel on older Fiats, you don't need a puller or to use a big hammer, simply loosen the central nut a few turns, then grip the wheel on each side (left and right), push down on one side while pulling up on the other, then do the opposite, as if you were trying to rock the wheel on the steering column - it'll pop loose. When refitting the wheel, be careful to align any pin on the wheel with the indicator switches (self-cancelling feature) and mind you don't bend any horn contact strips.
If after setting the front tracking you continue to experience steering problems (e.g. pulling/wandering to one side) or excessive tyre wear, it might be worth checking the rear tracking (idk the settings) and also to check that the front and rear wheels on each side are still in correct alignment (not so easy due to the different camber angles etc), maybe use a straight edge/plank/length of string or find a puddle in an otherwise dry car park and drive through it slowly while someone watches the tyre prints left behind on each side.
Professional garages with modern 4 wheel alignment systems should be able to get all the settings spot-on providing the operator knows what they're doing and
cares
Hth,
Al.