No no no. Don't "show" the character in terms of writing out a character synopsis like an excerpt from your story. You're supposed to tell rather than show. And believe it or not, agents like formality so long as you "personalize" it with a humble yet professional tone (don't address it to "Dear Agent" for instance but to the agent's name directly).
What they mean by showing is that they don't want you to strictly talk about the plot and mention only that the "hero" or "heroine" is involved. They want you to immediately introduce your character by name, tell who he/she is in as few words as possible (they appreciate writers who can limit their thoughts to a few words-shows word-smithing and efficiency skill), tell what happens to him/her (which should be the initial conflict of the novel), and describe one or two choices the character makes (and the consequences), to give the agent a well rounded summary of what this story is all about. Basically, it should read something like the book's synopsis that is printed on the back cover of the book.
By the way, the way you describe San is exactly how you do it. You tell it in a sort of cinematic way. And if San isn't a major contributor to the story then leave him out and simply state that the character sifts through relationships on her way to completing her goal (this is vague since I don't know your story plot line but you get the idea).
And by the way, literary agents don't read hundreds of query letters a day. Publishers and editors do. Popular literary agents may receive this amount but most don't. They are middlemen and new writers often try to solicit publishers directly, without so much as looking up a literary agent to help them query a publisher.
If you want something catchy then don't embellish your query letter. They like *SHORT* letters that get straight to the point, that have a humble tone, that answer all of their questions/guidelines, that are professionally written with no basic spelling/grammar/typo errors, and that demonstrate that the writer has an understanding of the book selling industry. If you write that "it's the next block buster hit/best seller" then they're going to scoff at you (especially if they're the NYcity big wigs), and they'll look for reasons to disagree.
So just follow the guidelines, include only what they asked for, keep it short, don't come across as egotistical and over sure of your success and you should be fine. Good luck with it.