According to Jack Lynch, whose book The English Language: A User's Guide is well worth the modest investment for those without the patience to deal with the OED or Fowler,
Many people get spooked by the plurals of proper names, but the rules aren't that different...The only difference between proper and common nouns is that the proper names ending in -y shouldn't change form in the plural: just add an -s. The members of the Percy family are the Percys, not the Percies.
Lynch goes on to warn against pluralizing with punctuation:
Resist the urge to put an apostrophe before the s in a plural, whether in common or proper nouns. The term for this vulgar error is the "greengrocer's apostrophe," from the shopkeepers' habit of advertising their "potato's" and "apple's."
If one has in one's company a multiplicity of persons named Jess, then indeed they are "Jesses". The same spelling would apply in the case of two or more persons yclept "Jesse." They too would be Jesses.
The questioner asserts that "English is silly," which I think is an unkind thing to say about anyone's Mother Tongue. English is sometimes fickle, sometimes illogical, occasionally intractable, but it is capacious, flexible and alive. It tolerates confusion. In figurative and humorous usage, English even thrives on confusion. Comfortable speakers of the language use it as a platform for invention and improvisation.
In the questioner's example, wherein we have a hyperabundance of Jesses of unspoken origin or character, it is likely that one or more of them will have adopted or been given a nickname by their peers: "Spike," "Peach," "Two-Step" or "Four-Eyes." The possibilities of human interaction, mediated by English, are nearly endless!