Another approach to increase the probability for running a 13.5K air conditioner witlhout having to deal with a heavy generator could be to use paralleled Honda EU1000i generators.
As has been mentioned, the steady state output of a Honda EU2000i is 1600 watts. However, the steady state output of paralleled Honda EU1000i generators is 1800 watts. This setup, along with the starter kit, may pretty much guarantee being able to power a 13.5K air conditioner.
What you also get is of course 120 volt AC backup for smaller loads due to two generators being available in case one should fail and - maybe more importantly - you have to lift only one 29lb. generator at a time.
The cost would be lower than paralleled EU2000i generators and higher than a single high power Champion generator, but for those with physical limitations the weight to lift would be the lowest.