First of all, I’d like to say that you come across as someone who is committed, serious and who takes the time to plan ahead. These are all good qualities for a teacher to have.
So, down to the nitty gritty! You say you want to work in Europe but that is an enormous area; so I can’t really give you country-specific advice. As you quite rightly say, many countries start the academic year in September and chances for jobs are higher in September and January. You should also look at countries such as Poland and Czech Republic where the academic year is split into two sections: one starting in September and the other in February. Depending on the country you apply to, you have the option to get a job in January or February. In any case, in private language schools, almost anything is possible. They are far more flexible than state schools. What’s more if you let a new employer know about your plans with plenty of notice, they should be able to find a solution that allows you to have a long weekend. You could swap lessons with a colleague, change a timetable slightly to allow you to have a long weekend, a colleague could cover for you and you repay the favour at a later date.......
You could go ahead with your plans to study in November/ December. Apply for teaching jobs for January and February. If you find a job, that’s great. If not, look for alternative employment and try again in September or apply to summer schools in the UK which start around June/July.
You say your job ends in November; I don’t know whether that means you have the option to continue in that job after November or not; you can give all the above some serious thought before you decide whether to leave your job in November. I hope I have given you some food for thought and there is no reason why your project shouldn’t work and you can still go home for the wedding.
All the best,