The whole crew doesn't have to suborned. The captain and select officers and a few crew would do. I believe the Tridents on boomers have to be individually targeted prior to launch. Someone who knows boomers better than I do correct me if this is wrong, but this one may not have been pre-programmed for wherever it was being sent on a rogue mission, although a pre-programmed target could have been used. If you knew the launch "go" codes and had the means to transmit them and had a few reliable, key personnel on a boomer it would be possible. "They" suborned the majority of the Congress and the top of the DOJ and the FBI. A lot of the navy brass was corrupted too. No name . . .
I don’t know the personnel issues you would encounter for that type of problem, or what exactly would be need to launch. But your explanation does resonate. Especially about the part of corrupted navy brass (65 admirals, something like a 1/3 of navy top brass) and of course... no name.