It's not a matter of the quality of the glass, removing the adhesive layer has nothing to do with it, because you will most likely have replaced the lost adhesive (unless you've done as some of the youtube videos described and used the old adhesive, even so, that would have left less space between the glass and digitizer, invalidating one of your point of the air gap). Chances are you made the same mistake I did, if you heated the adhesive to long or held the heat gun at the wrong angle you probably melted part of the digitizer or LCD (probably both, because they are part of a single assembly on this phone.) I make this presumption based upon your last description stating that the screen is less black when turned off than originally, mine is the same. If you did inadvertently melt the digitizer that would explain your issue with responsiveness, once again, mine is the same.
See step 9 to see the glass being separated from the housing AND from the LCD.
The LCD is not fused to the glass... Once you loosen the adhesive, you can pry the glass off, CAREFULLY, the LCD will not come out, it's only the outer perimeter that has the adhesive.
Are you talking about the iOpener heat pack? If yes, I would recommend using that instead of the heat gun, but nothing would really make it easier. Watch out with the heat gun if you use it, heating the adhesive too long will result in damage to the screen.