Yes, the hover function interferes with layer click event. What you can do is add a click event to the map's graphics
function clickMap() {
map.graphics.on("click", function (e) {
console.log(e);
console.log(e.graphic.attributes.ProjectNum);
});
}
You'll also have to add the attributes of the feature to your graphic in your layer mouse-over event
var highlightGraphic = new Graphic(evt.graphic.geometry, highlightSymbol, evt.graphic.attributes);
Is there any reason you have two map load event listeners running?