If it doesn't want to go into park, it may be the issue that the button does not lift a pin inside the stem (tube) of the shifter high enough to clear the step of the 'combed' gate. I know 2 variant of shifting pattern exist, but I can only describe my own version:
The rear gear selection is blocked ( in my may 73 cs) with a horizontal pin that lifts and allows clearence over the 'combed' black shifter support. This pin is threaded in the middle, and connects the the vertical rod inside the selector tube. The pin is lifted when you push the button on the side of your gear selector.
The stem of the selector has a slot that allows the pin to move upward.
In the picture you can see it resting in the forward slot; the parking position.
For reverse, it needs to travel to the back, and thus lift a bit.
The tube itself also has the large fine thread above the chromed section.
When reassembling the lot, there are thus two threads that need to catch.
The inner one needs to be connected first. You probably need to hold the pin up with two fingers as high up in the slot of the tube as you can to get it to catch while spinning the entire selector. When it catches, you can lower the selector and screw it on the tube. I am not sure if you should or should not push the button on the side of the selector while getting the pin to catch.
You can check easily if it the pin is connected after installation; there should be a few pounds (~30-50 newton's I guess) of resistance when pushing the button. If it did not catch the pin, then the knob on the side feels way to light (no resistance).
if it is connected, and still doesn't want to go into park, then something else is wrong.