Hi, just some advise....don't rent, satellite phones are really not that expensive, especially if you get an older model Kyocera SS-66K. I have one that I'm selling at the moment, I've used it when I was traveling, I'm going to liquidate it for some cash for some other stuff and buy another one some other time before I travel, which is the best way of doing it if you need a sat phone that way you get it MUCH MUCH cheaper than rip of rentals.
Iridium is the only satellite network when is truely 100% global - anywhere on the planet earth. I'm selling the phone for just 475 euros, you can get small, medium or large pre paid cards for airtime credit, I can help advise you on the cheapest supplier too which I found and I can arrange it for you too.
I will send it anywhere, just pm me for a shipping quote shouldn't be too much.
I'm based in Ireland, I've used it in egypt and thailand so far and its been perfect for what I needed it for.
If you look at Thuraya coverage map you will see that it will not cover the Pacific (not fully) or the west coast Americas. I'd say Iridium or Inmarsat would be your only options, and you already have fleet broadband so Iridium would be good to fill in the gaps, I don't know of any Gsm/Iridium combo. I'm going to pm you the pictures of the phone.
Paul