It wasn聮t that long ago that the world thought we聮d all be using satellite phones by now. But their expense, the massive improvements in coverage for traditional mobile phones, and the inability of satellite phones to scale up to data demands (such as the iPhones need) spelled their semi-doom.

I say semi-doom because there is just enough demand for them from people such as yourself to keep them around. They certainly are handy in those remote places where you just can聮t use your wireless handset.
But the convenience doesn聮t come cheap. A sat phone kit such as (chargers, handset, and battery, plus phone) is $1,500. That is not a typo. And that is the phone you need聴it聮s extremely tough, reasonably compact, can handle chores such as e-mail, and is meant to keep you in touch anywhere on the planet.
Things don聮t get any cheaper when you add service; $150 a month will get you聟120 minutes of talk time. Two hours. Additional minutes make a ka-ching sound to the tune of $1 a minute.
But, if you need it, you need it, you know? And you obviously can afford to do some pretty high-end travel, so my guess is that this might fit your budget. I do hope you send us a photo at some point.