What is a good way to humidify a (temporarily) vacant desert home?
I suppose if you want to pay for the electricity to run your furnace, A/C and humidifier all summer while you are not there, that is certainly an option. But if you consider that all these parts have a service life, do you really want to spend 50% of that service life running them when you are not home?  There's also the problem of if it breaks or otherwise stops running, how will you know?  And of course, your A/C will be working to dehumidify the environment which might be the opposite of what you are looking to accomplish.

My in-laws have a place in the desert with lots of wood furniture and they always just leave buckets of water out and so far have not had any issues with cracked wood.  It sounds like this is a cheap and reliable method.  Perhaps you could find someone who can check in on your house after a few months and fill up the bucketes if needed.