I also think "gramex" is a bit clunky. But grammars mean parsing. I assume that "parsex" would be a bit too "volatile" and open to unrelated criticism.

The shorter "parex" might be about right; there might be wars about the "correct" pronunciation ("Parsing :: parex." "No! Parrot :: parex!"). So what?

Eventually, of course, we'll all want to shoot the person who puns about the "parex par excellence!" for the thousandth time...