Heat pump mini splits should work fine. If you want service in the bathroom, you could consider hiding a small air handler and running very short ducts.

You should consider changing building or modifying the building design to something that works better in your climate. A cool metal roof will probably serve you better than shingles.....

Thanks very much for the reply, ionized. And I think the cool metal roof is a great idea... :)

Mitsubishi, Sanyo, Toshiba and others have some good presentations on the web of the types of indoor modules available. You should probably familiarize yourself with the high wall-hung, ceiling-mounted, air handlers and other before calling contractors. Pay attention to the controls as well. There are differences between the manufacturers.

If you do decide to go with ducts, they should be inside the envelope. You can put them in the attic, but in that case, you should seal the attic and insulate the roof deck. That might not be a bad idea even without ducts up there.