The style of safety on your gun is, in my opinion, a significant improvement over the previous design but it is a little tricky getting it together without bumping the linkage out of position.
The order of assembly does need to be done as you have been doing it.
With the button in the safe position and the linkage carefully centered in the corresponding blocked position carefully fit the two assemblies together.
You should be able to tell if you have the correct engagement.
If you are having difficulty with the toplever spring, one solution is to drill a small hole in the receiver on the right side under the lockplate located to intercept the leg of the toplever spring. Tap for number 6 machine screw. Then at any time a #6 screw can be threaded in to compress the toplever screw.