I'm on small twins at the moment (and loving it by the way!)
Legally you need 700hrs of which 100 is multi to fly single pilot in the UK, so I'm sure it'll be the same in the rest of Europe.
Do you speak french or German, because if you don't then your chances in those countries are pretty much nil, also the chances of you being able to live and work in Switzerland are pretty small.
In my opinion the main problem you'll face (except converting to JAA, which is hard and time/financially consuming!) is competition, I'm constantly being asked by instructor friends if my company is taking anyone on, and I'm sure lots of operators are constantly hounded by CV's and phone calls.
If you realistically wanted to get work over here on twins I'd recommend 1500hrs total of which 500 is multi, and you'd still be lucky in this current climate! We don't really do single engine charter like you do down under as we cant guarantee VFR like you guys can!!