is there a countdown widget which could be used so that users could see the deadline for submitting change requests per sprint?

Galliwell

It would be nice if this were configurable so that after "zero hour" is reached the clock can be made to change colour and continue counting negative. In this way, you could show that CRs post zero hour will be considered under extreme circumstances. (eg avoidance of a Priority 1 defect etc) 

unknown

There's no built in JIRA gadget for what you describe. The closest thing I can think of (out of the box) is the Agile Sprint Health Gadget, take a look at that. If you don't like that, you can always create your own gadget.

Reference: https://developer.atlassian.com/display/GADGETS/Developing+Gadgets