“AND saying Amein w/o kevanah is a real averia is for sure worse then learning and not saying amein at all.”
????
See Magen Avram in Kuf Chaf Daled, where he brings down a machlokes rishonim whether one must stop those who learn during chazaras hashatz. One opinion is yes, and one opinion is no, IF they are answering amen. NOT answering amen is not an option according to any opinion (the nosei keilim discuss how wrong it is to be mivatel answering amen). As an aside, someone who has the head to learn at this time, certainly has the head to have the proper kavana to answer amen, so really it comes down to, is it better to lean, or to answer amen properly, and you seem to be coming down on the side of “talmud torah kinegged kulam”, so is OK to be mevatel answering at least 19 amens in order to learn.