The issue you're having is that you're trying to test over 7 dimensions, with the majority of those dimensions being irrelevant to an individual taking the test to signal mastery of 2-3 of them.

The standard method in testing to deal with issues of this nature is to provide people with the opportunity to test themselves on modules, rather than taking the omnibus test so that they can spend the majority of it signalling that they aren't good at things they don't care about. If they're good at everything, they can sit for all of the modules. If they aren't, they aren't wasting their time.

Additionally, this frees candidate time up to let you test people in more depth in the areas they're actually professing skill in. From that point, you're open to do interesting things; evaluate question difficulty/time to completion and adjust the questions provided as the test unfolds to match the expected skill of the applicant for instance.

As it is now, you're getting buy-in from corps that little have no skin in the game, but I don't see how the sample test you have provides more signalling value than an applicant having a CS degree or a list of github projects they can discuss.