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After a few test prints and some measurements, I wanted to share that I think the threading you have for the Base Socket is wrong. I believe they are 1/4" threaded pipe (which doesn't mean either the internal or external are 1/4" FWIW). Most of the pipe I've found online (Amazon, Ebay, etc.) advertise the threading at 1/4" PT (pipe thread) but don't indicate which kind.

I was able to get a very nice matching print using BSP G1/4-19 as the threading, but it may be an MPT 1/4" thread instead.

BSP: https://en.wikipedia.org/wiki/British_Standard_Pipe
NPT/MPT: https://en.wikipedia.org/wiki/National_pipe_thread