After a bit of research, the Moodle plugin Achim mentioned in his answer (that enables one to import questions as new versions) will work to fix issues with questions in live assignments (although, it will still be a bit time consuming if one has lots of instances of the problematic question).

Since the Moodle plugin for now only allows one to import one question as a new version of a single question, if one has n instances of a question, one would need to generate the XML and import as a new version for each of the n instances one-by-one. The random seed would need to be set to ensure the same random values are used in the old and updated versions of each instance.

One thing to note, if you just go and import the XML with each single instance as a new version, you will be met with the error "Exception - Your file did not contain exactly one question!" (even if your XML only contains one question). To get around this, just remove the highlighted lines from the XML where the category is specified. And then it will work from there.