Seems to me it was you who made a big deal over cutting edge. You asked a question, got a couple of answers. You didn't like those though, didn't fit with your thinking
Ummmm, no.. Someone else suggested using a 747 would be "quaint" and not at all "cutting edge". I challanged that notion.
If cutting edge image isn't too important then I would imagine a C-17 would be ideal.
A C-17 could not begin to meet all the requirements. A C-17 is about the size of a 767 externally, and a 4-engine 767 simply could not meet the requirements.
Although technically, a few C-17s have ALREADY been Air Force One. Air Force One is the call sign of ANY airplane with POTUS aboard, and Clinton, Bush, and Obama have all flown on C-17s.