Data theft via remote desktop connection
Use FRAPS to capture video from your local machine.  Then you can flash stuff up on the remote desktop at up to the frame rate and it will all get recorded to a local video file.

I don't see a way to sync to exactly to the frame rate, so you'll need some error detection to make sure you're not getting data mid-draw.  Here's a simple scheme using text and a python script:

framerate = 30  # fps of viewer
numlines = 24   # lines of text you can see at once
import sys,time,md5,base64
lineno = 0
while 1:
  lines = 'chunk starting at line %d\n' % lineno
  for i in xrange(numlines - 2):
    lines += sys.stdin.readline()
    lineno += 1
  print 'md5:', base64.encodestring(md5.new(lines).digest()),
  print lines
  time.sleep(1.0/framerate)


Run this script in the RemoteDesktop window and pipe in the text you wish to capture.  When it is done, OCR each frame of your FRAPS output (that's the hard part, I'm not sure what you'd use for that).  Throw away any duplicate frames and frames where the md5 isn't right.  

You probably want to base64 encode your input, as OCR doesn't do well with nonprinting characters like tabs and spaces.