How to reduce a nut from 32mm to 9.8mm
Modifying Paul Logan's comment, use a close nipple  and cap , but instead of drill and tap, just drill a hole large enough in the cap to insert the stem from the socket - tight but don't damage the threads - then take a nut that fits the stem and attach it from the inside of the cap. If it's hard to tighten it, fiddle around with some washers sized appropriately.

You could also lock it down by using 2 nuts. Put the first one on all the way next to the one holding the stem onto the socket (in your pic), insert the stem into the cap, put the 2nd nut on getting it as far as possible inside the cap - finger tight is fine - then then tighten the first one on the outside. And bobs your uncle.