Be careful with the chains. I obviously know very little about these but here's my 2cw. I looked at buying a set for my 265/65's just before last year's Lesotho trip, but decided against it because of the capital layout for ONE trip. Later I realised that it would've been worthless anyway because there isn't enough clearance between the tyre and the bearing carrier (suspension upright).
I know you get those low-profile chains, but the only approved chain sizes for the Treg are 235/65R17, 235/60R18, 255/60R17 & 255/55R18. I suspect you might have serious difficulties with fitting chains on a 275 tyre. (Maybe we should have a look at the Cayenne's chain options...?)
If you want to make provision for chains, I think you'd have no option but to go for the 245, but then I'd rather go for the 70-profile Yeti's got. The 65 is going to hamper your performance in sand, which I think is what you are more concerned with.
Then again, there seem to be very few people here that actually DO fit chains on their Tregs, so maybe you should stick with the 275 choice and forget about the chains. (Easy for me to say, I know...

)
Or go with the in-between 255/60R17...? (I'm not helping here, am I...?)
Also, keep in mind that the increase in foot print size when deflating is actually more due to an increase in foot print LENGTH than width. This means that a narrower tyre with a much larger profile can actaully end up having a bigger foot print than a wide tyre with a low profile. So there might be a smaller difference in sand performance between a 245/70 and 275/60 than what you expect.