To get an "exemption" you have to have tested positive (with official documentation showing the positive test - i.e. not an at-home test) AND have a note from a doctor certifying that you are "fully recovered" and "cleared for domestic and international travel." Your positive test has to have occurred within 90-days of your cruise (but cannot be 12 or less days from the cruise as that is too soon to have fully recovered). So, if you tested positive 95 days from your cruise, you would not qualify.
And yeah, the freebie gov't tests are rapid antigens, so they are not the best and can show false negatives. However, they are free and better than nothing. I plan on getting a rapid PCR test (same test they give you at the port) the morning we leave for Orlando, and also have access to mail-in 48-hr PCR lab tests since I'm a gov't employee, so I will probably do one of those say 20 days out or so in case I have a lingering positive from an old infection I did not know about.
Basically I'm going to test myself as many times as I can in the days leading up. I have not been an overtester, and during the entirety of the pandemic have only been tested 3 times (all because my work required them for me to come back due to a close contact). I am, however, prone to stress and overthinking so I'm hoping the tests before will help give me SOME peace of mind that I won't hit positive at the port. Or at least give me time to adjust my plans if needed.