In regards to the values that you are using for the search.x and search.y it should not matter. Normally these values come from the button that was pressed, when you use an image to submit a form the coordinates of where you clicked on the image are passed with the name of the image and .x or .y. So you are just simulating a click of the search button by having this in the link.
As for editing the menu file directly this is definitely the way to go for adding in the parameters for the links. So long as you are getting to the results page with the correct results displaying for the category and sub category it seems that you have it worked out.