I have 2 Air Lite - Tanto and Drop point, both close okay. I even tightened the pivot all the way down, they still snap close pretty crisp. I've had the same issue you described for other models(i.e. storm cloud), 2 reasons that could cause it:
1. The lockbar not seating correctly and is contacting the blade stop pin before it contacts the blade tang. This is often due to the lockbar pivot isn't well finished/smooth enough for it to rock forward and back. Unlike normal backlock with round lockbar pivot, triad lockbar pivot is oval to give it space to rock slightly forward and back to "hook" blade in negative angle. The "hook" is what made triad lock so strong, not just the stop pin contrary to popular belief(
side note: this is why i hate when people said Triad lock is just a backlock with an extra stop pin). Try adding a couple drops of oil on the lockbar pivot in the middle of the handle as well as around the front "face" of the lockbar where it contacts the blade stop pin(the pin the blade contacts when open). Oiling both side of the lockbar helps too. It should be pretty easy to get to these area. Open and close a few times after oiling.
2. You didn't remove the paper thin layer of teflon washers did you? This is another reason why this might be happening. Removing the washers could mess with the tolerance and cause the lockbar to grind or stuck on the G10 scale, which stop it from hitting the tang because of lack of space. I used to have this issue a lot because i like to remove the teflon washers from all my CS folders. If you remove teflon washers you'll need to replace with a 0.01" washer to maintain tolerance, because the thin bronze washer is only 0.006" thick without the teflon.
Finally, not usually the cause, but you can check if the spring is seated correctly. I've never seen the spring move out of its area on triad folder if assembled correctly, but it doesn't mean things can't go wrong during assembly. I've disassembled both my Air Lites multiple times to replace the washers and clean their innards. It's built pretty nicely mechanically, so other than the above mentioned issue something else need to go very wrong to cause your issue.