FYI the US EMbessy has a non denominational service once a week for americans wanting to worship as they want....They've had some big ads running in JEMS and EMS Magazine for a few months. Here's the website:
http://www.emssaudiarabia.com/
I looked and considered, for a bit - personally, I'd miss a few things, biggest of which would be the freedom to pray in a house of worship for my religion.