You didn't state which of the three releases (not the same as version) of the Twine 2 application you (or your students) are using, and that can make a difference on the answers given.
eg. was it the
a. Download & Install-able Executable release.
b. The Hosted Web-browser based release.
c. The Downloadable Local Web-browser based release.
d. Some combination of a,b & c.
...had trouble installing illume...
After looking at both Illume and Entweedle I believe that this issue (#421) is the cause of your problem, because both of those story formats have the same version number (1.0.3). While the cause of that issue has been fix in the Twine 2 application's repository, that fix won't be available to the public until the next release of the application.
note: I don't know when the next release will be but I do know that a new beta build of the application appeared on the application's repository on the 31-oct-2017, so the next release date may not be that far away although that date may depend on how long the testing phase takes.
Is there a fix to this chaos...
If you were running the install-able executable release of the Twine 2 application (or even the local web-browser based one) then I would suggest editing the related format.js file of one of the two story formats in question and change it's version number to something other than 1.0.3 (eg. 1.0.3a) so that the two didn't have the same value, that way the 2.1.3 version of Twine 2 would correctly accept that the two story formats aren't the same one.
note: This can also be done with the Hosted Web-browser based release but that requires editing information within the local storage of each user's web-browser, which is a more advanced activity.
Another possible quick fix is to contact the developer of the relevant two story formats and asking them to change the version number of one of two to something other than 1.0.3 (eg. 1.0.3a), that would also cause the v2.1.3 version of Twine 2 to consider them two different story formats.
...a way to easily get Twee from Twine 2
Unfortunately unlike the (semi-unrelated) Twine 1 project the Twine 2 project currently has no official support for TWEE notation (neither the importing nor exporting of it), and I don't know of any current intent to add such support. There is also no easy way to convert between a Twine 2 and a Twine 1 project, so you can't use Twine 1's built-in Import/Export TWEE features.
note: Programmatically it would be a fairly simple task to create some sort of script/utility to convert the story project file of the Install-able Executable release of the Twine 2 application into a TWEE notation file, because the data of a story project file is a very simple HTML like structure although some care is needed to convert some of the Passage encoded content back into plain text.