G&L Tribute legacy HB set up problem

Hello to everybody!
I've been happy owner of G&L Tribute legacy HB Indonesia. I purchase it used and guitar has some minor issues (non working ton pot and some light scratches from previous owner) that I thought will be no problem to fix by myself.
So, to get it in to preferences, (I prefer light strings and low setup) I replace strings with Gibson #9-42. And then i noticed that tremolo position looks wrong.
I look over this forum and found setup guide, which I had used and here is results:
Tremolo is parallel to body and 3,17 height from it. Setup like in guide.
The #6e is 0,018 from the 1st fret.
Truss rod set up as in instruction and #6E is 0,012 from #12 fret.
But then it goes wrong
When saddles on the bridge in lowest position (laying on top of the bridge plate) the #6E is about 0,79" from 22 fret. In manual it has to be 0,62" when right adjusted and in the same moment #6 bridge must be 3,17 from bridge plate. I tried it and it became about 1,4" from #6 to 22 fret! My model has no micro tilt, so it is no other way to lower it more in my opinion, but to lower the tremolo to the body by tight 2 screws that holds it, but I'm not sure it is the right way to do.
I did check neck. It is straight. I took it off. Seems nobody did nothing with it from fabric (it has stamp with date of production on it).
So, maybe someone of you did faced with problem like this. Maybe models with 4 screw neck has some other way to adjust neck angle and string height? Any suggestion? Thanks!

Yes, I would just start with a .020 thick shim between the two screws next to the end of the neck and the body. That will lower the action and ideally you do not want any saddles bottomed out. If that doesn't do it, use a thicker shim. I generally use brass shim stock as I have it. Make sure that you don't overtighten the neck as that can cause issues in itself. -You seem to have done everything correctly, it just needs a shim and that is not uncommon. I have done it to several of my AMericans as I like low action.-- Darwin.

As Darwin said, one doesn't want the saddles "bottomed out" against the bridge plate. Before shimming, triple check the two bridge height adjustment bolts to make sure they are correct. American measurements can be confusing. Translate to the more sane metric measurement if that helps, then try again.

I want you to check because your measurements seem off a bit. You typed #6E and #6e, so I'm a bit confused. The high note e is #1 and the low note E is #6 just so we're on the same page. It's confusing I know and I'm sorry. Better still, let's do this.

Here we go. Loosen the strings to half tension, then level the trem plate at 4.76 millimeters and insert a wooden block, or whatever fits that won't scratch your guitar, of that height keeping it perfectly level to start. Then measure 1.78 millimeters string distance from the BOTTOM of the string to the TOP of the fret. If it's a bit more, it's OK. If it's less, perhaps we have issues. Then tune the strings to pitch. Now, here's the trick. Now you must go back and forth adjusting the strings and the springs in the back of the guitar (sorry those words are so close) until the balance just holds the block placed under the trem with little pressure. You want the guitar in tune and the spacer just secured lightly at this point.

Now we have a starting point. Has this been done already? Do this, then we will continue.

...triple check the two bridge height adjustment bolts to make sure they are correct.

But, curious: exactly what constitutes "correct" spec when it comes to the height of those two bolts?