IPhone – How to take a screenshot in iOS without hitting the Home Button and the Power Button

Take it to the Apple Store. Tell them exactly what is going on and that it's a real problem for you. Even if they can't recreate the problem there in store, they will replace the device. I had a similar issue with my iPad. I took it in and explained everything and even though they couldn't replicate it they replaced it.

If anything, they will help you get a resolution. I've never gone into an Apple store with a problem only to have them tell me "Sorry, nothing we can do."

screencapture has a -R option for specifying the area. It is not mentioned in the man page but it is mentioned in the help message:

$ screencapture -h
screencapture: illegal option -- h
usage: screencapture [-icMPmwsWxSCUtoa] [files]
  -c         force screen capture to go to the clipboard
  -C         capture the cursor as well as the screen. only in non-interactive modes
  -d         display errors to the user graphically
  -i         capture screen interactively, by selection or window
               control key - causes screen shot to go to clipboard
               space key   - toggle between mouse selection and
                             window selection modes
               escape key  - cancels interactive screen shot
  -m         only capture the main monitor, undefined if -i is set
  -M         screen capture output will go to a new Mail message
  -o         in window capture mode, do not capture the shadow of the window
  -P         screen capture output will open in Preview
  -s         only allow mouse selection mode
  -S         in window capture mode, capture the screen not the window
  -t<format> image format to create, default is png (other options include pdf, jpg, tiff and other formats)
  -T<seconds> Take the picture after a delay of <seconds>, default is 5
  -w         only allow window selection mode
  -W         start interaction in window selection mode
  -x         do not play sounds
  -a         do not include windows attached to selected windows
  -r         do not add dpi meta data to image
  -l<windowid> capture this windowsid
  -R<x,y,w,h> capture screen rect
  files   where to save the screen capture, 1 file per screen