I also vote for doing some riding before major changes, but I personally am a mere mortal, so a 45x20 low gear would limit me to pretty flat ground.
Doesn't sound like your part of Switzerland is super flat, either.
I don't know that crankset's bcd, but the lowest cost/risk might be to swap chainring down to a 39, and then potentially cassette. Sheldon's site mentions that doing the 6 to 7 change allows megarange cassettes. I went that route; it did mean a new RD and wolflink. But I got as low as 39x34, a big help from my 42x24. The megarange is effectively a 6-speed 14-24, plus bonus
#7 34 bailout.
One of many options, of course, but my investment was low to find out whether I really liked riding the bike.