Running in new tyres takes 200 miles or so, this completes the vulcanisation process to give the maximum road adhesion, afaik ,and also removes the slippery mould release compound.

Importantly, you should adjust your tyre pressures to those recommended. Don't necessarily trust the tyre fitter.

Just a thought here, those times you found the steering going light, was it afternoon/early evening after several days worth of salting without rain?

I ask because when the salt has sat on the road for a few days, it attracts the damp as the day draws in and the surface can become as slippery as the ice it's there to help keep at bay.

A few weeks before Christmas i had just swapped over to the winter wheels and tyres on SWMBO Forester, a car that usually never puts a foot wrong, one afternoon i popped out in it and at the mini roundabout up the road the steering went decidedly light and the car felt like it would run wide, that immediately put me in mind to change the tyres, but i decided to see how they fared..sure enough once it rained and washed the roads clean again normal proverbial grip returned.