I would thoroughly re-research the sigma 12-24, I've heard bad stories about it - and especially on 3rd party lenses, the 5D3 will show you all the problems with corner sharpness, CA and vignetting that, as an aps-c-user, you've so far only read about
My aps-c UWA (Tokina 12-24) got replaced by a 17-40 when I got the 5D3, which is roughly as wide - but I don't use it as much, because the 24-105@ff has a divine reach.
About the 28-300 - it's very bulky to call a 'travel lens', very heavy too. Don't think you'll be wanting to lug that around for days on end - speaking of which, just why is your friend selling hers?
Both the 24-105 and the 70-200/4's are half its weight - your bag won't be lighter, but what you have in your hands will. And you're in for a bit of a shock to see just how versatile any 70-x00 lens is at full-frame - so I too second the suggestion to buy the 70-200/4IS over the 28-300, unless you really hate switching lenses.
Mind you, switching from 300@aps-c to 200@ff is a serious detriment to your tele reach. Happened to me too, I don't mind as much since I don't shoot tele often, but I just got me a 1.4 extender all the same. Of course, there's lots of good stories about the 70-300L too, but the 70-200's are legend for a reason