I have heard back from Cisco support that despite their education connector saying it supports "other" LMS tools, it will not support Blackbaud and currently there is no roadmap laid out for the integration or support for this feature. While it might support others, and even provide the "other" option for integrations, currently it is not a supported use-case for the product. It is very unfortunate to see the education connector not support an LMS that is LTI v1.3 compliant...
All that being said, I have been in touch with the Cisco partner, CirQlive and they have an off the shelf platform that is able to offer what I need and much more.