currently I am flying for an American airline...
You must have the legal right to live and work in the US then? I mean you got what other people are dreaming of?! Looks like you managed to work your way up the latter, at least quite a bit.
...and wish to change my licence over to an EASA ATP-L.
Apparently you have not the slightest idea about what you're getting yourself into! I've already been there, where you intend to go! Looking back from my personal experience, I have to say I wouldn't do it again! Especially if you are already in the business, meaning you already fly for an airline and are building valuable time on a jet which can/will advance your career.
In short, you need to prepare for and pass all 14 EASA ATP exams, which is just a big pain! Don't underestimate it, like the vast majority does! It takes a lot of self-discipline, determination and motivation! Duration anything form 6 month (usually for a full time class) up to 24 month and even more (commonly for distance learning courses) and working a full time job besides studying. As mentioned, it's quite a challenge! Better think twice and consider all possible options!
Preparing for and passing the skills test (known as check-ride in the US). Things are different here in EASA land and they'll let you know it! Generally you need to fly a minimum of 15 hr (plus some multi time) can't remember the specifics anymore! But this will be quite an expensive experience, I'm telling you!
Additional you'll need an EASA medical, general radio telephone operator license (AZF) and if you intend to go for a german EASA ATP license (which I'd strongly advise against doing so) the famous and absolutely stupid "reliability check" (zuverlaessigkeits-pruefung) which is required by the German LBA.
However, assuming you're flying for a regional in the US? If you're not happy with your current situation, for whatever reason. Why don't you consider going to the middle or far-east and fly there? Allegedly airlines are in need of qualified pilots over there and the compensation packages appear to be quite tempting, compared to airlines in the EU or Germany. And most importantly they won't make you jump through hoopes for converting the license.
Anyway, good luck!