This is quite a fanciful proposition. I can't imagine Feynman being 'installed' in any position, by the government or anyone else.
Before the Manhattan Project, Feynman was an assistant prof. at U. Wisconsin-Madison. During the war, he was on a leave of absence from this position while he worked for the Army. After the war, Feynman had taught at Cornell U. in Ithaca, NY for 5 years. He had turned down an offer to work at IAS at Princeton because he wanted to teach. Eventually, Feynman chose to accept an offer from Caltech, in no small part because of the climate, because he hated having to put tire chains on his car during a snow storm at Ithaca (from his autobio "Surely you're joking, Mr. Feynman").
Certainly, if the govt. had wanted Feynman or any other scientist 'on tap', they would have found a position for him closer to DC. It is difficult to remember now, but during the war, Feynman was not as big a deal as he became later in his career. He was a newly minted PhD. who was an assistant prof. at a midwestern state U. in 1942 with no atomic energy cred. It wasn't until long after the war that he began the work which led to his Nobel Prize, and he was not one of the scientists who worked on the H-bomb, having become depressed following his work on the A-bomb..