Within the free ad platforms, I found flatfox.ch to bring a very good number of candidates

You only need to offer 1 person who is willing & able to take over, if rejected then you are free. Why give a choice?

Print out your good photos, with a sketch of the floor-plan, and the price and date.
Put one of these flyers in the letterboxes of the 10 buildings closest to you. Or: if that printing is too costly, then at least hand-write your add about 20 times and tape the ad on the bus-stop, and on the central door of each building near you.

Anyone who already lives there and likes it may know friends or colleagues who would like to live there, too.

I already payed for this month and if I leave they can take my deposit, I don't mind that.

They can also come after you and that would not be good. One never knows for future prospect of working here.

They will pursue it and you will be blacklisted if you ever want to come back.

They will try to find you one way or another and the amount will rise and rise.

But for each one that 'get away with it' there are just so many foreigners who will find it even harder to find somewhere to live, as the agencies and landlords will say 'they are just too much touble' - and that is tragic.

Come after me and do what? But I don't want to break the law, I just want to find someone and get on with it

You haven't even lost your job yet. I get that you're worried but take a deep breath. If this employer made the effort to hire you then another one might too. All is not lost.

Edit to add - Landlords also have obligations under the rental contract. They can't simply kick you out because you have a hunch you'll lose your job.

Yes, but also finding someone is a total headache.

Not necessarily- and it is what it is.

It does seem as though you have made up your mind though.