But that first example from Oxford English: "Not nearly enough for the social positions which they had to keep up." That's a fragment, not a complete sentence, so I'm a little confused as to how it proves a comma isn't needed?
(Then again, I most often exist in confusion.

)
Lol, okay, I'll defragment for this:
It wasn't nearly enough for the social positions which they had to keep up.
And if we write the example as both restirctive and non-restrictive:
Restrictive:
It wasn't nearly enough for the social positions which they had to keep up.
Non-restrictive:
It wasn't nearly enough for the social positions, which they had to keep up.
Hard seeing why it can't just have the comma right?
Say them out loud and see how the commas affect the nouns around it:
It wasn't nearly enough for the
social positions which they had to keep up.
It wasn't nearly enough for the social positions,
which they had to keep up.
If you bring in another trick here, you can pin down what's happening.
Restrictive use (without the comma) can drop 'which' and keep it's meaning:
It wasn't nearly enough for the social positions they had to keep up.
non-restrictive 'which' can't be dropped:
It wasn't nearly enough for the social positions, they had to keep up.
Dropping the 'which', it changes the meaning (you're left asking 'they had to keep up with what?')
it shows that 'Which', in non-restrictive usage, is a noun subtittute for the noun previously mentioned, in this case 'social positions' and you can't leave a non-restrsictive noun out without messing up meaning:
It wasn't nearly enough for the social positions, the social positions they had to keep up.
It wasn't nearly enough for the social positions, which they had to keep up.
So the restrictive phrase 'which' is 'narrowing down' the reference to the noun social positions (it's not simply providing additional information).