I have been running stair laps ever since I smashed a kneecap in a cycling accident over a decade ago. (I lost an argument with the curb on a sidewalk!) It is really intense exercise but i have found nothing else even comes close to providing your legs with the explosive push you need for short steep hills as well as the sustained effort you need to climb alpine passes. Find a small football stadium or indoor basketball facility; or run the stairs in a building that is 4 to 8 stories in height. Run up taking two steps at a time, and 'jog' back down one step at a time. Start at 10-15 minutes, and work up to a maximum of forty minutes over the next two or three months. Stay at 40 minutes until you are within two weeks or so of leaving for your tour.
A stairmaster is a poor substitute but will work in a pinch. Simple reason. On a stairmaster you never go 'down' (although the effort level can be adjusted. So your knees never develop the muscles needed to 'hold you back' (the ones you feel when you walk down a steep hill). Thus the muscle buildup is unbalanced. If you use toe clips when you ride (i do not...just a pet peeve) you'll be glad your legs have those muscles in good tone.
Running stairs has worked wonders for me. I end up laughing my way up big climbs like the Great St. Bernard or the Karakoram Highway! It lowers your pulse rate (mine is under 60), and greatly increases your lung capacity (i have 40% more lung capacity than the average 46 year old). It keeps you on the balls of your feet, which is what you push the pedals with. Short of cycling itself, there is no better preparation for a cycle tour.
In London and many backpacker haunts in Europe you will see ads "for backpackers insurance" that covers all sorts of things, including theft and yes, repatriation in the evnt of illness or death. If you are under 26, these may be very worthwile policies to buy for the peace of mind they give you. Policies vary: check with the various providers.