Question: Where specifically on the arm/hand should rapid picking speed come from?

Answer: 
There are likely as many routes to fast picking as there are pickers... For bluegrass-type fast runs that are mostly done in a pretty strict alternate-picking style, it seems to come from the elbow with the wrist relatively rigid.
Doc Watson refers to "picking from the elbow" when digging in on such passages.

Note that I'm talking about steel-string acoustics here, and usually set up with rather stout medium-gauge strings.  

Playing an electric with "slinkies" can be quite different.
The pick type makes a great difference to me - if I'm chugging I'll use a fairly thick pick, but for speed I'll go for a 0.4 or 0.45 mm pick, and as new as possible...if it is worn you have to move it further to get the point of the pick past the string to return back across it.