Your paranoia amounts to a lot of good entertainment.
As a Mormon, I can assure you (99% sure) that Mitt would not choose to swear an oath for office over the Book of Mormon. I suppose he could take that route, but it would be entirely out of character.
You really should read the words of Ezra Benson (Secretary of Agriculture under Eisenhower) on Mormon views on their role in government. His words should hold as much weight as any current or former Mormon prophet. After all, he was the Mormon prophet from 1985 to 1994.
Found here:
http://tinyurl.com/3278hbPerhaps if you twist it just right, you'll be able to use Benson's words to further your agenda!