David --
Remember, this is just newspaper style we're talking about, not Holy Writ. If you want to call it the 1st Annual, go for it.
In common usage (albeit incorrect, according to strict constructionists of the language), calling an event the 1st Annual whatever is understood to mean "the first of what is expected to be an annual event." However ... what if you don't have one next year for some reason, or have another one six months from now? Then calling it the 1st Annual whatever looks a bit silly.
But be advised that whenever the second one is scheduled (or not), calling the first one the 1st Annual may turn off newspaper editors and TV/radio news directors whom you are courting for publicity. You could call it the Inaugural Gulfport Oral Cancer Screening, and play off the sense of celebration associated with that adjective. Or just call it the 1st Gulfport Oral Cancer Screening. Either is accurate, and neither implies a time frame for a second event.
In answer to your question, if you wish to follow AP style: If you do this a year from now, it's the 2nd Annual Gulfport Oral Cancer Screening.
OK, putting my blue pencil away for now. (That shows you how long I've been doing this ...)