This case is an older style, having a screw on cap over the neck of the case. The sleeve and stem just sit loose in there, held in by the cap. In this instance, the cap does not screw down all the way on to the top face of the neck. When the cap is on all the way, it leaves some space. You can see this in the photo by comparing the height of the cap with the length of the threaded portion of the neck on the case. The sleeve and stem assembly can move up and down inside the space left inside the cap.
Everything else works and fits. If a new, shorter cap could be found, then the stem would have to be shortened because the crown would stick out too much. As a general rule, we never alter existing parts to match a replacement. So what I think will help to to add a spacer inside the cap to fill the excess space.
Here's how the new part will go. It's a quick job to return it to the lathe to cut is down a bit and round over the top edge so as to conform neatly inside the cap.
Here is the finished and cleaned up spacer and the cap, separate and in place.
The case finally assembled, the cap snug against the top of the neck as before, but now with no free space inside and no up/down play.