Cover letter to a prop firm

Hi guys, i've written an application to a prop firm - junior trading position (london), pretty elite even by street standards in terms of # of applicants vs. places offered. My CV is solid, exam academics are good, but a bad uni result from a top uni (UK), is the only slight tarnish, but can be explained. Lots of places that insist on a high uni result have interviewed and previously offered me a job.

My issue is with the cover letter. I can do a standard, motivation vs. job requirements, neatly filling in all the boxes, but that style isn't really me. The place i'm applying for takes people from all walks of life as long as they have done something exceptional (which while i havent got a nobel prize or anything, have a few good things on my CV).

I've drafted several paragraphs for the cover letter, and am debating which ones to put in (all in would make for a lengthy or incredibly short read).

What i'd like is some feedback whether these are good points for this type of cover letter or bad ideas that my warped mind has conceived. The topics are in *'s, my own comments are after the - .

You recruit able people from all walks of life and thus any team formed from such a group will be more innovative and productive - This is genuinely my strongest reason. I love companies that have an open mindedness approach are awesome and get amazing results.

Part of the Job Des. is Strong quantitative + analytical abilities, extraordinary communication, negotiation, and interpersonal skills, and an exceptional sensitivity to detail are essential. - Is it a good idea to give examples for all of these/some of these?

Entrepreneurial - It isn't mentioned in the description, but I can't see how it is a bad thing. That said, it was a reason i was rejected from my HR round interview at a big prop firm recently. Does including this make it look like I ignored the job description?

I want to give the impression that I love all things strategic, how far back is acceptable? I was school and county chess champion at a young age, national champion for bridge for the rest of school and in the England team at university, plus a top ranked gamer in some top RTS titles. keep in or omit?

Extraordinary attention to detail: This is probably my biggest surpise asset. I worked at Buckingham Palace once (summer job), and did something there that was completely beyond the call of duty but is now used as an example in staff training. Is that a bit too unrelated? I can give some examples from trading too, but which is stronger?

Autistic end of the spectrum: How is this viewed? They say and emphasise they dont discriminate (this isnt my issue at all - I dont believe they would), but my logic/numeric interests comes at a price this time. I can do the standard party tricks associated with this (dont need a phone book, can remember EVERYONE's birthday (without facebook), last job i had (big 4) commented on it when i was picking numbers from accounts without looking at them, they thought I wasnt taking it seriously :( ). I dont see it as a disability, at all. Some people are good are some things, and bad at others, just my particular combination has a name. You wouldnt know by talking to me, I hide it pretty well. I'm worried they might see it as not good interpersonal/communicator, which isn't true but preconceptions might ding me before they speak to me.

I can see that last part wouldnt go on a cover letter, but should it be included with the rest of the application (there is space for it).

This firm is an unusually good fit for me (I think) so I dont want to screw this up. Once I get an interview I can handle rejection, but it's really galling when you just want to scream at them that you're right for the job (i wont try it), but get dinged because something good in my head didn't come across so good.

p.s. no mention of integrity at all on the website, should i mention or is it a given?

Thanks in advance, you guys are usually really helpful, if you can guess the name of the firm please dont say it :)

T