"They ride 700c bikes in most parts of the world i've been to. I don't think there'd be a problem getting spare tyres anywhere, even though they'd not be the best tyres, obviously."
By all accounts you will find it almost impossible to get 700c stuff in Central and South America. What parts you will find will only be for racing bikes. There is no reason not to build up an LHT with 26" wheels, it will make your life so much easier.
A friend was just touring for 3 months in Mexico. A few days in she crashed in busted her front rim. She was able to get to a town close by who had some 26" rims. They rebuilt her wheel and she was on her way within a couple of days. This would not have been possible with 700c.