You need to think about starting current too. The AC unit will draw momentary inrush current as high as 60 amps at startup (locked rotor amps) and you will get more initial voltage drop and the unit may not start. I would consider a hard-start capacitor and I think you may also need to go up another wire size or two to allow for startup.
Info. on Coleman (for example) showing startup current here:
Coleman I can't see why using a step-up and step-down transformer won't work as long as it's all done correctly. But the cost of doing all of it could be more than the extra copper cost. May be worth pricing out tho. As said, aluminum could be an option but it needs to be one wire size larger to carry the equiv. current.
What is the voltage at your panel like and how stable is it? That could be something to take into account as well.
I couldn't find info. on what a hard start. cap. would do to the required wire size, but here is info. on Supco:
Supco hard start caps.It looks to me that you need min. #6 copper for 250'. It looks like #8 Cu would give you 96 volts at startup, if you started at 120 volts, and that's too low.
This info. indicates that starting voltage should not be less than 10% based on 115 volts which is 103.5V.
Advent AC unit info.
