Not sure that actual question has been answered. Others can/will pipe in, with their experiences.
I believe the issue is around the SXM EHAS vs. SBH. Fully vaccinated and boosted, you will be able to complete the EHAS form, with no testing report required, 72 hours or less before you travel. What we just learned from Maryella was that, absent the booster, with a COVID history, she needed to get test results to complete the EHAS form.
As far as the eMed test, it has worked for most of us for SBH. We didn't run into issues, but we were fully vaxed, and did not need to report anything related to testing when we completed the EHAS, so it was not an issue for us, for the transit through SXM.
Hopefully someone will be able to speak to their actual experience, having success with the eMed test, when completing the EHAS, absent the full vaccination protocol.