I'm not sure my exact notice period. I basically was in this situation where I had to wait a completely unpredictable amount of time for the authorities to grant a new permit for me to change jobs. This means I told (by email then discussed verbally also) my current job I accepted the new job a couple of months ago already. I said that once the permit goes through I'd like to be able to start the new job on the first of the following month. It's a fixed contract and I only have one more month anyways but would like to switch jobs now (not work that final month).

What are my options if they drag their feet now for some reason? Am I basically forced to tell the new job that I can't escape my current contract, and so need another month before I can start? I started interviewing with them in December so it's really been a long time to wait already.

Maybe I am stuck? If I had been acting more cautiously I would have perhaps given notice unconditonally and had a gap between the two jobs. My reason for not doing so is a) I discussed with them about mutually terminating and it seemed fine and b) I was afraid the gap would mess up my residence or work status in Switzerland. Now in hindsight I should have considered and planned the worst case. In fact the situation may be fine, maybe I get released from the contract quickly, but I like to know where I stand.

Would this be a dispute situation where I would have to go to a labor dispute board of some kind? I would rather just negotiate. I would even sacrifice the previous month's pay or something like that; I really intended only to do the most secure thing in terms of my work status in Switzerland because moving out of the country would be expensive and very inconvenient.

Theoretically what would happen if I start the new job without release from my current contract (and stop working my current job)? Would I be breaking some kind of law by having two concurrent contracts? If there is nothing preventing me from doing this, then it would be a fine contingency plan. I obviously would be fine if they then said I breached the contract and didn't pay me that last month (or even another month's pay on top of that like I said).

I expect they would be okay with negotiating and coming to some mutual agreement, but maybe they are regulated in such a way as to be too inflexible to do this. Or maybe they wish to make things difficult despite my openness to negotiate, so therefore I just wonder what my options are. Hopefully things go smoothly and they are communicative as I try to sort this out with them. Even then, however, I am quite interested in how this situation could play out under Swiss law.

Talk to your employer again. New employers are usually aware that notice periods exist. Do you have any vacation time accrued?
Generally speaking if you break a contract the other party can sue for loss. They wouldn't pay you and if they suffered extra costs because of your absence they can sue you for that loss. It really depends on what it is you do and how quickly they could find a replacement.
If this is like a working from home job where you're not very busy and no-one would notice you working abother full-time job then I'm not sure how that would go down with the authorities. As you *could* be on holiday from the first job then I would suppose it would be ok.