Your dilemma sounds like an excellent case study for migrating to an LMS that can manage everything from SCORM to xAPI.
Because you know what the output measures are that you are seeking, that helps a great deal. While it's true that SCORM can provide that data, your LMS may not be processing the package(s) correctly because of its own inherent limitations or architecture. So I would suggest that you explore what the LMS can do - another opportunity for strong vendor relationships, perhaps, or maybe replacing your current system.
We did a major update and migration last year (to SuccessFactors) and have had some positive results achieved with tracking the data through different LMS quizzing features. Ideal? Nope. Good enough (reliable) to get some data that we can stand on? Yep. Are we able to explore the steps needed to get to using xAPI? We can, but "we just upgraded the LMS so we are not pursuing any further migration paths for the foreseeable future." Sigh.
