Well played, OP. I remember that horrible sinking sensation of people nudging each other and gossiping, and am sharing this story in order to empathize. In my case, it happened when I was sexually harrassed (and later stalked) in my workplace and I reported the abusive creep and it all went down formal channels and became very unpleasant. Amazingly enough, the worst of it happened after I reported him and suddenly found myself a pariah. Members of my department were asked to witness to his behaviour on record, and I was later able to read those reports. When I did so, I cried and was physically sick. They all sided with the abuser, minimizing my account and preferring to believe that their eccentric, 'lovable' colleague couldn't possibly be a sex pest so therefore it must be the woman (me) who was lying. I ended up on protracted sick leave because of illness caused by the stress. When I returned to work, for a long time I was the one wanting to hide in a corner whilst others sneered and blanked me, which infuriated me because I'd done nothing wrong whatsoever. And as in your case, the evidence was all there but the truth didn't matter. They'd chosen their preferred narrative, and that was the end of that.
A few years on I'm still here. I don't give the time of day to the colleagues who decided to side with a sex pest (who was, BTW, hoofed out). What I learned from this episode is that life's an unfair bucket of shit, and I got this additional truckload of it thanks to having the temerity to have been a victim of harrassment and abuse. How dare I assert my own boundaries, protect my bodily autonomy, stand up against a sex pest, and ask my employers to exercise their legal duty of care?
I felt awful for a long time; doubtless you will too. But now I'm flying, and doing better than ever. I breeze past the ex 'demi-friends', greet them, but don't engage in conversation. And I no longer give a flying bison's backside what they think. Soon, neither will you. And that's a promise. You've handled this like a champ. 
