Robert,
I am not sure if this will help you or not, but it may help point the Azure support folks in the direction to help you diagnose the problem.
Checkpoints and backups are both forcing writes to the file system. IO is notoriously slow in virtualized environments. It could be that Azure IO performance is really bad (in which case your out of luck), or something in your Azure instance configuration or current state that is causing a slowdown when file writes occur.
I would be interested to know if you do get a resolution to this problem, as I have not heard of it before.
--Jason