Your question is actually a perfect storm in which rules of puntuation dictated by grammar clash with the deeper grammar of spoken English, though rarely with the noun in your example.
Unless you are in the unfortunate situation of having only one single solitary friend in the world, in your example the proper name Adam is a restrictive appositive, that is, ...
Without more substantial rephrasing, it will sound strange even if it is technically correct.
It would be more natural if you simply drop the use of the possessive:
Here is the completed assignment of my partner, Jane Doe, and me.
This seems to be a pertinent question as I haven't seen this discussed in any grammar or on this site.
When the noun phrase ends with a noun we are quite happy to put an 's on the end. This is often described in grammars as the "King of Spain's daughter" or some similar phrase and is discussed on SE here. However, since the 's can only be added to a noun, ...
You would say "John was my grandfather". This is because when he died, he essentially stopped being your grandfather, so to speak. It is like if being a grandparent of parent is an occupation, like being a carpenter. You would say
"John was a carpenter."
Likewise, you would say
"John was my grandfather."
You are describing an attribute of the listed item. It's position in the list is secondary to the attribute.
"The/An attribute of the first of those listed."
"The [attribute name] of the first of these."
If they are distinct things in the list then the attribute's position will be clear.
"Of the bird, the mule and the horse the color of the wings is the ...