I have a similar problem in my condo. Third floor, 16' vaulted ceilings, very poorly insulated.

Summertime temperatures are always in the mid 80s regardless what I do with the windows.

I have two portable units. One in the bedroom so I can sleep. It is ducted out the window. The other is in the living room ducted up the fireplace chimney. I have a huge volume of air so nothing is completely cool all 1500 ft.?. I like the portable unit because I can put it away in the winter. I can still use the windows, horizontal sliders, and it is much better at directing the air where I want it than the old 'through the wall' type did I still have installed but rarely use.

Another advantage is the HOA in my complex has regulations about how long you can have window units installed plus the size and color. My place will stay hot well past the time that I would have to remove a window unit.

The biggest disadvantage is having to drain the condensate tank occasionally. Window units drain right outside.