Here's a pure Python implementation of the Burnikel and Ziegler recursive 
division algorithm.  I've no idea whether it's faster or slower than 
Newton, but it might be worth a look.  It depends heavily on bit 
operations, which ought to be much faster when coded in C.  (Some of the 
shifts would be completely unnecessary---replaced by changes in indexing 
instead.)

The original paper describing the algorithm is available here:

http://cr.yp.to/bib/1998/burnikel.ps