You've got the passport which is great, how is your Dutch or German? They do prefer the local language speakers, so if you have that, great. I am not familiar with the hiring practices of KLM or LH, but I believe it's quite comprehensive.
A year should do for the exams. Best get the medical done first so you have a reference number for correspondence with the licensing authorities. As for the practical, it would depend on which type you are the most comfortable with and having to arrange a sim ride that's observed. That will be expensive. Far more so than in the US.
Personally, if you've made it into the majors already, you have time on your side to ride a few boom/bust cycles. I'd squirrel as much money away for when (and it is only a matter of time) so when the inevitable down turn happens, you're ready for it. The US majors have much better T&Cs than Europe, especially money wise. Bide your time, save some money, go part time and commute.