The Century Dictionary and Cyclopedia defines Singular as meaning:
- Out of the usual course; unusual, uncomon; somewhat strange; a little extraordinary: As a singlular phenomena
More literally it derives from single, meaning one, so a singular phenomena is logistically something that is assessed as happening just once. It is of course possible to use the term hyperbolicly or mistakenly, which can diminish the effect, but I doubt you will find any word that lacks that particular problem. The nature of hyperbole is that people tend to exaggerate, and sometimes intentionally, so they will choose whichever word most effectively achieves the exaggeration they want to convey.
Since the dictionary entry was written, Singular Event actually overtook singular phenomena in popularity as shown by google Ngrams, and collins shows that singular is one of the top 10,000 words used in the language, so I figure that this demonstrates that it is more than common and easily enough understood.
Regarding singularity event❌, the reason that does not work is because the suffix functions to change the adjective into a noun, as noted by the entry for -ity:
A common termination of nouns of Latin origin or formed after Latin analogy, from adjectives, properly from adjectives of latin origin or type, as in *activity, civility, suavity etc., but also in some words from adjectives not from latin origin or type, as in jollity. The suffix is properly -ty, the preceeding vowel belonging originally to the adjective. See -ty2.
Sometimes adjoined nouns do modify nouns, but much more rarely than adjectives and in a very different manner.