Don't make this more difficult than it needs to be; there is no good reason. Just put a regular vibrato on, set it up to act as a hardtail, and go to bed happy. If you can actually hear a difference in a blind experiment, then you should get a job in audio forensics, or become a Sonar Tech on submarines, not waste your magical God-given ability by being an electric guitar player.
Another option is to just sell that body and buy a hardtail one. You can often get them off the shelf from Guitar Mill for under $200. I got my ash hardtail Strat body there for something like $140, already made. The time and energy you spend jury rigging some [again, unnecessary] solution for the body you have is worth $200, IMO. Plus, if you sold the body you already have, you might be spending under $100 for that new body in the end.