I don't understand why there is double charge, if my understanding is correct, so there is $100 application fee plus $150 exam fee (menbership) that total $250 for a specialty exam fee.....

The one “elephant in the room” problem that I personally see with LEED, is the fact that so many AP’s used for certification are actual employees of the design and / or construction companies for the project.
LEED certification should be a totally third party system, which, with the vague exception of the HVAC Cx, is not.
Even the Cx can be an employee of the firm, as I understand, but cannot be part of the original design team. Not sure how that works!
The LEED AP’s working at the design level should not be the same AP’s who process the submittals for certification. The submittals should be handled by an independent consulting firm.
The way it works now, the foxes are counting the eggs in the henhouse.