I was going to convert my FAA ATP to a (f)ATPL in the UK but got a job where my FAA license was good so did not finish it, did all the exams but none of the flying.
If you just came to the UK to do the conversion it would take you the best part of a year, six month minimum for the exams via distance learning and the mandatory month of refresher in house teaching.
You would then probably spend at least a few months doing the flying and would then have a grand total of a whopping 650ish hours which would not put you near the top of any airlines recruitment lists.
You would then move back to the US once you found it impossible to get a descent flying job in Europe.
What you should do is accept the offer, spend two years instructing and get a FREE conversion. By the time your two years are up you will probably be getting close to 1500 hours and a US ATP. You can then look for a job in the EU but will also meet the requirements for regional FO jobs in the US, you are far far more likely to get a job in the US as an FO. If you still want to get to the EU keep building your multi crew turboprop/ regional jet FO time and eventually a job will come your way in Europe.
To be honest doing it any other way is total madness.