Are there any exceptions to the obstacle analysis requirement?

Yes, but they are very limited. One exception is outlined in FSIMS 8900.1 Volume 4, Chapter 3, Section 5, Paragraph 4-599, which allows certain small, light aircraft (under 19,000 lbs) to deviate from obstacle clearance requirements under strict conditions. This does not apply to larger aircraft like the Global Express or to high-elevation airports such as Eagle.