The suicide and body moved thing really doesn't work.
If Foster had killed himself somewhere else, the movers would have also moved the implement he used (gun, rope, whatever) to Fort Marcy Park with him.
If Foster had killed himself somewhere else, there might have been a real suicide note.
If Foster had killed himself somewhere else, the xrays wouldn't have had to disappear.
If Foster had killed himself somewhere else, no one would have felt the need to alter the death certificate.
If Foster had killed himself somewhere else, he probably wouldn't have picked a day when his sister was flying in from out of town to see him.
If Foster had killed himself somewhere else, the President might have once referred to his death as a suicide.
If Foster had killed himself somewhere else, the President might not have spoken of "Foster's failure to protect himself" in the eulogy he delivered.
I could go on.
ML/NJ