Yes, I'm definitely going to learn how to build a wheel. In fact I'll take the whole bike apart and put it together again when I get home.
I don't want to use a bike service ever again, I haven't had a single good experience with any of them. I think each bike shop that I've taken this bike to has broken something in it.
I think I'll only do another 700km on this trip, so I'll just go with what I have. I'll by a few replacement spokes for the new wheel. They are all new spokes, so should last me that much, even if they're not tensioned correctly.