Right. Either relativity or our understanding of quantum mechanics had to be "violated" in order to explain their observations. Einstein & Co. chose the latter

Right. Either relativity or our understanding of quantum mechanics had to be "violated" in order to explain their observations. Einstein & Co. chose the latter with their idea of hidden parameters (i.e. information already present in the second particle). But, later experiments based on Bell's theorem seriously challenged the hidden parameter explanation, preserving quantum mechanics in the process. So, that takes us back to instantaneous information transfer or a third option: one electron (or any particle for that matter)!