I have to wonder if the test the person you spoke to was in relation to their (SIU’s) Apprentice program. That seems to be their default response to persons looking to join the union.
As far as getting a job there be advised the SIU uses the hiring hall/seniority system. Yes, you have to go to a hiring hall. The SIU has 3 levels of membership, C Book (starting out), B Book (mid level and Apprentice Program graduates), and A Book (Full member). Any B Book will beat out a C Book when throwing in for a job. A Book will beat out B and C Books. As sea time is accrued ones moves up.
Once you get time and move up from wiper to QMED finding a job gets easier.
You might want to consider MSC, NOAA, or ACOE. Try contacting the companies @Wasforkandblade suggested. It might not be the deep seas career you are looking for, but it will get you passed the entry level rating you currently have.