well . . .
reading the various user comments on the LPA sights for this weapon . . .
some say the OEM front sight worked fine
I replace the rear sight. the rear sight, bottomed out, puts the bore laser 2-3 inches _high_
the LGA sight is 'taller' that the OEM - so apparently as S-W has not a single clue as to how to make a sight, I will now replace the front sight and see if the adjust-ability thing works.
I have owned several Shields. I've had no issues with any of the sights. I think the gun is hitting that way for you for a few reasons. First, you are not using the right sight picture.
Second, I've found that the original and 2.0 version of the Shield is almost TOO thin. I too would often shoot to the left without extra effort on those original width Shields.
Now, the Shield Plus has a slightly wider grip. To me, the Shield Plus grip is perfect. I love the Shield Plus grip. I sold my Shield ver 1 and 2.0 once I got my two Shield Plus pistols. I knew I would never carry them again after getting the 3.1" and 4" versions of the Shield Plus Performance Centers guns.
I had the same issue with the Springfield XD-E. I had to put WAY too much effort in the perfect grip... And concentrate way too much to shoot the gun well. It was really TOO thin...
I have other guns I can pick up and shoot with zero effort. For a self defense gun, you don't want something that takes that much more effort. So, I sold the XDe...
Not every gun is a fit for each person. That's just life. The thinner Shield may not be for you.
Look at the Shield Plus. See if you can rent one. The Shield Plus takes zero effort to shoot well. It may fit you better.
Be aware too, that your method of sighting in the handgun with the laser is not realistic. Boresighting with a rifle is useful to get on paper. Then, you fine tune the sight manually to dial it in all the way. And, it can be ammo specific. You can't only do a boresight and expect it to be perfect.
On a handgun... Remember the bullet does not travel in a straight line. Also, many laser bore sighters are not made perfectly. The lasers are often made off center. Every rifle laser boresighter I have ever owned has had the laser off centered. If you spin the housing, you will see the laser move to a different location.
Unless you are mounting a red dot, no one uses a laser boresighter to sight in a handgun with iron sights.