Touring on a fixed

To each their own.
For me, I think it's total fucking nonsense even riding the less steep parts of the alps on a fixed touring bike. Uphills will be hard, you will have to get off and walk, downhills will be slow because you won't be able to spin fast enough.

It's a matter of fitness and gear ratio, run one for climbing and one for descending, could be 49/20 and 49/17.