Your shifter is correct and complete than. I just pulled and measured mine, same thing.
It could be the two pins in the side of the tower that locate the shifter, are they worn badly? They should fit he slots in the shifter with no play idealy, although some is to be expected.
If not that then I would start looking at the shift rails and the slots that the shifter engages in them.

Is it actually locking it in two gears at once, or what exactly happens when it does this? start from there and see what it takes to do it again and that should show you what is wrong now that you know you have the correct shifter.

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-