Why do you want to convert (or do you mean validate) your license? Just stay with the FAA PPL and gain experience by flying N-reg aircraft.
AFAIK the war against pilots being EU citizen and holding foreign PPL only has not reached the point where they forbid flying on that license.
If you are short on budget just gain experience and postpone IR for later in the US. And yes, with US immigration authorities, it may be unwise to enter the US during Greencard processing, but the American Way may be easy - simply approach the relevant authorities with your story and ask ... As EU voting cattle we tend to forget that other governments may work for their (potential) citizens ;-).