Well, I'm sure the OP's head is spinning by now. If he's still with us, I'm not going to attempt to add more advice on top of all the stellar if not somewhat conflicting advice that's already been offered. Of course, then I still end up writing way more than I intended below. Well, anyway, read on if you like...
A situation just like this is what got me back into serious amateur photography. Good friend, casual home wedding and just a borrowed 30D, one zoom lens, flash on a bracket and my own Digital Rebel. Me and my wife took a bunch of pictures and I was hooked again. (That was almost 4 years ago and I'm not sure I want to look at those pictures now. Guess I should though just to see how I did compared to my current knowledge level since then.)
My point is that all the advice so far falls into two camps, run away or do your best along with details to support both. Only you can decide what is best based on your relationship with your friends and your comfort/courage/knowledge level. Sounds like you made a wise decision.
My vote would be to go for it as you outlined and learn from it, enjoy it and see what you can do. I also own a 6D and from what you listed, you have a great collection of gear for your needs. If you don't want to buy a big flash, don't. However, you might consider a small SunPak RD2000 tilted up with a StoFen diffuser to use as fill. Turn it off or on depending on what you think at the time. Let ETTL do its magic and use the Flash Compensation setting to dial it down. (I set Flash Compensation as the SET Button function for easy access on the 6D.) Maybe set the Flash Function in Av Mode to Auto so the ambient light will balance with the flash more evenly (but with a much slower shutter speed). Keep it simple
. Don't take every lens. Put the 17-40 or 28-75 on your camera and get all the pictures you can. Move around a lot. Encourage people to get together, smile and wish the couple the best. Shoot what's comfortable. Push your limits but don't get a migraine doing it. You can fix a lot with Lightroom. Use available light if you are comfortable with that.
Bottom Line, don't try to be a "Pro Wedding Photographer" because you aren't. Neither am I. But you can perhaps be an amateur journalistic photographer with some practice and prep. Be that. Before the wedding, try to surf the web and look at all the images you can of wedding receptions, party events, etc. Get posing ideas. Get composition ideas. Practice in the days leading up to the big day to help put yourself at ease. My advice is to take what you can from BOTH camps of advice in this forum thread. Just be you and prepare however you think works for you. There's a ton of advice here, use what you can and let us know how it goes, maybe even post a few pics!
Good Luck and May The Force be with you!!