Help - Adjusting ‘67 904 console floor shifter

This thing is driving me nuts. The trans is professionally rebuilt (‘76 Volare), originally a floor shifter and the shifting mechanisms are all new.

I put it in Park, shove the lever on the trans all the way back to Park position and tighten the linkage rod. Park works fine, move lever to Reverse - it’s still in Park. Move lever into Neutral and it goes into Reverse. You can the partially select Reverse and it stays in Reverse. Neutral is Drive, push it back a little over half way back, it’s finally in Neutral.
I don't think you are getting the complete travel cuz the shifter button won't let the shift lever move all the way into the "P" position, as I mentioned earlier.
In the description above, it seems you don't get to P in forward position, your description describes starting the shifter gates in "R", and all positions after don't get to 1
Unscrew the shifter button a few turns, try forward travel WITH BUTTON PRESSED , then unscrew a few more, check travel WITH BUTTON PRESSED .
You should end up getting more forward movement, with a click/lock into "P" you weren't getting before.
That is Park.
That's all I got .
Have you got the shifter button screwed on to the correct position to allow full travel of the actual shifter lever.
See the gates and button release lever at bottom of shifter.
If the button is screwed too far down, or not enuff, you may not be getting full shifter travel, ? ?
I know you say your getting 1 & P, but are you ?

EDITED !