Does WordPress still use GD for manipulating images?
As far as I am aware, yes.
Thanks, esmi! It appears that you are right. GD is now working and my images are cropping fine.
For future reference, the problem I had was that every time I tried to yum install php-gd, I received an error telling me that no such package was available. This was resolved by rebuilding PHP in the WHM, using EasyApache – enabling the GD module on the Exhaustive Options List.
A more detailed account of why this problem may have arisen (WHM ‘excluding’ GD from yum updates) is available here.