I'm noting a trend... multi-part continuation fics which take place in
a
completely new setting (i.e. college) with a completely updated cast
of
characters. So, which came first, KOR or DNR?

KOC by a long shot.  We started waay back in 1993.

I could've sworn KOC started 1992 or so, because DnR definitely 
started in 1993 or so, and I'm fairly sure there were six episodes 
of KOC out at the time.  

We did some revisions to DnR in summer of 1996, though. Mostly 
because the Ranma manga ended then.

But for continuation series in fanfic, KOC is pretty much the 
granddaddy.

-David Tai