Just tested with import and a window extended beyond / bigger than the screen size; and it seems import will capture an image of the same size as the big window size -- unfortunately all pixels beyond the screen size, and all pixels covered by other windows, will be black.

So maybe the only way is to use xrandr to enlarge screen size (as in 'screen pannning') - or to use something else that will provide larger screen size: for instance, "How can I take browser screenshots at a higher resolution than my browser supports? - Super User" notes:

Use Xephyr to create a nested X session

(Xephyr is apparently in sudo apt-get install xserver-xephyr in Ubuntu)

Hope this helps,
Cheers!

Edit: yup, xrandr works with the usual printscreen for me (also with import, just needs enough space for a terminal to fit, so it doesn't overlap the target window), just note the Virtual size in xorg.conf (see "xrandr: screen cannot be larger than" ...)

I believe Screenshot Captor is the tool you're looking for. It involves a slight learning curve though and the scrolling window capture feature might seem intimidating at first.

It can capture objects, meaning content within windows with scroll bars (horizontal and vertical), individual program controls, etc.

It is quite powerful but some tweaking with the settings may be necessary to get what you want and hence, the learning curve.

If you try the program and it doesn't work for you, before you dismiss it, watch the videos listed on this page, especially this one about basic scrolling window capture.

Here's an example capture of a scrolling Windows Explorer window (click to view full size):