I did similar to adapt a TH400 to my 65 Impala. I use all the stock 65 Impala Powerglide linkage, except I use the piece from the kit, shown in your photos, that attached to the shifter shaft on the transmission.
It's interesting that your kit included the deep hex nut, called a coupling nut, pictured here -
https://www.grainger.com/product/1JE...g!109231852677!
I had done the same swap on my 69 Chevelle, with a TH400, and you could use a 3/8" - 16 standard nut, and a socket would go over it to tighten. Unfortunately, at some point GM changed the threads on the TH400 shifter shaft from standard to metric. The 10mm nut is ever so slightly larger than the 3/8", apparently, so no-go in that tight spot with a socket or wrench. Of course, the TH400 core I built for my 65 Impala had the metric 10mm x 1.5 nut, and a socket would NOT fit into that recessed area on the shifter arm to tighten the nut. I had to search around and find a 10mm x 1.5 coupling nut.
SO - moral of the story - if your TH400 core is an early one, it will have 3/8"-16 threads on the shifter shaft, and any old 3/8"-16 nut will work. If your TH400 is a later one and has the 10mm x 1.5 metric threads on the shifter shaft, you MUST use a coupling nut in order to get a wrench on it to tighten it, as shown in the photos above.
Anyway, hopes this helps someone down the road from having to figure this out all on their own like I did. It was pretty aggravating
