Fodshaker, the hold on the gun can indeed throw shots low left for a righty. Make sure you're using a firm two-hand wraparound grip (not with the left palm forming a "saucer" under the "cup" of the firing hand). The tighter you hold, the less likely you are to "milk" shots low left. Milking occurs when the other fingers sympathetically tighten with the trigger finger. If those other fingers are holding as tight as they can already, they can't tighten anymore sympathetically.
However, the first thing I'd do would be to readjust your laser sight. You mentioned that you set it up for point of aim and point of impact to coincide at 20 feet, and were getting low hits at 60 feet. Because the laser beam emits from below the barrel, when you get farther than 20', the line of the laser has crossed the line of the bore, which will put the laser dot progressively farther above point of impact as distance increases.
This may also account for leftward straying of shots, as a tendency to hit lateral that might go unnoticed at 20' will be more pronounced at three times the distance.
Try re-sighting the Laser Guard to send its beam parallel to the barrel, and make sure that it's centered laterally with the shot group at 60'. With that set-up, you'll always be hitting an inch or two directly above the dot, and will know where the shots will go at any reasonable "combat distance."
Give it a try, and let us know on here how all that works for you.