I don't think you can go wrong with any of your choices
These are 2 very closely matched offers. Triumph made it that way :-)
I test rode both - liked both and ended up buying the BMW f800gs - it feels more like an enduro :-) (very subjective)
I was lucky enough to get a used one that had almost all the stuff I wanted on it - incl. the monster Touratech Aux tank, which is a pain to install. Comparision tests showed that the BMW has a smaller tank, but uses less gas - so the range was about the same.
If you go used and you are short on time, you might find more BMW's out there than 800xc's, it's an older bike.
I think both have their shortcomings on suspension, which is something you might think about since you're going around the world 2up.
There might be more BMW dealers and independent repair shops tan is the case for Triumph.
Since height is your concern I think the Triumph has an adjustable seat, whereas for the BMW you have to buy the lowered seat. As you're ridin 2up, you might be better off looking for a aftermarket seat right away.
Hope all is well with you guys and the scare will wear off soon