Your expression "Unit: "+myArray[i]+"\\r.*?\\r" matches three paragraphs, so you can address paragraphs to access just the short title. It seems to me that you don't need to look for the English short titles first: simply look for two consecutive paragraphs that start with "Unit:", then take the paragraph that follows them. It's similar to what you do, but simpler:
app.findGrepPreferences = null;
app.findGrepPreferences.findWhat = "Unit:.+\\rUnit.+\\r.+";
myFinds = app.activeDocument.findGrep();
for (i = 0; i < myFinds.length.length; i++)
myFinds[i].paragraphs.appliedCharacterStyle = "...";
Thanks for your response Peter. Your snippet is simpler than what I was trying. I don't know why, but I was getting similar results with your snippet as I was with my own. For some reason, however, after completely re-typing the code in my script editor it worked great.