Mauro Nappolini, who finished the 2013 edition of the Tour Divide on a single speed 29er, has this to say about his experience.
Sorry for taking so long to get back to you, have been really busy. You could have not picked a better bike to single speed on. Just a little tip, carry both drive side and non drive side drop outs as I stripped the drive side drop out in Montana and rode some 500 miles or something like that to steam boat where I found a replacement. Im a bit of a techie and believe that the alphine is a designed for the road and possibly a bit of light gravel at best. If it was a day trip on parts of the divide I would say go for it, however being that you will find your self 100s of miles a way from a bike store that can handle something like the Alphine, and that there are only about 4 well stocked bike stores on the route I personally wound not risk it. If you are leaning towards the internal gear hubs I would check out the Rohloff hubs, the 2012 winner won on one and they have a stellar reputation of durability.
Are you a current single speeder? If I was going to do it again, I would definitely not ride a single speed. There was a hell of a lot of pushing, I mean daily pushing and some of the times for a few hours, real demoralising stuff when you know that you can be miles and miles down the road if you were on a geared bike. Please do not underestimate the amount of walking that is required when riding on a single speed. I have thought about riding again and if I did I will consider riding a dingle. I don't know what a dingle is so Ill elaborate, essentially its a two speed and possibly three speed manual single speed set up. So you have two chainrings up front for a 2 speed set up with 2 cogs on the rear, to correct the chain length difference the chainrings have 2 teeth difference between them, say a 34/32 and a 20/22 cog at the back. I have heard of a 3 speed working this way but the chain line may be a bit off and cause a bit of drag. The Salsa will be perfect for this with its vertical drops, quick and easy.
One thing to consider is what type of experience do you want? Is it more of a social experience where you can ride with cool guys if you want to and have a shared experience, Or is it more of a solo solitary experience. The latter suits the single speed, because it is difficult to match the speed of a geared rider with a comfortable cadence. I did ride with guys at times but most of it was spent alone, which was amazing.
I have now problems speaking to you via phone or Facebook chat, as I have a lot of tips to single speed the route easier as well as lots of tips on not making the same mistake I did.
Mauro, thanks for the advice.