Personally, I would favour a compact, or for lots of mountains a triple, but Adam's not going to change all that Shimano drivetrain, so I suggested the sprocket option.
39*25 is OK for the first 1 or 2 mountains (provided they are not Alpe D'huez ) then it really hurts.
I was amazed last year to notice that hardly a single ("foreign" - to me) rider on the Marmotte was using a 39 - ALL compact or triple.