I would like to control the location of matplotlib clabels on a contour plot, but without utilizing the manual=True flag in clabel. For example, I would like to specify an x-coordinate, and have labels created at the points that pass through this line. I see that you can get the location of the individual labels using get_position(), but I am stuck at that. Any help would be greatly appreciated. Thanks!

EDIT:

The above image is an example plot that I would like to apply this method to. The default label positions are inconvenient -- the flat areas between Day 2 and Day 4 would be more visually appealing.