There are two basic ways of getting to other star systems without getting cute with the laws of physics.

Slowboat: either a generational or hibernational system that travels at some small fraction of light speed.

Generational systems ("Journey to Alpha Centauri" or "Orphans of the Sky") have vast engineering problems, but nothing that screws with physics. The kind of hibernation that allows someone to stay asleep or frozen for hundreds of years is almost as outlandish as a stardrive, but still doesn't mess with physics. Really messes with biology, though.

However, as you already found out, the slow hibernation ship using "normal" propulsion works best for your story. Don't worry. "Star Trek" aside, nobody is really going to be able to track a hydrogen exhaust plume (fusion or antimatter) across deep space.

Relativistic ships: Don't violate the laws of physics, but if you're an engineer, you've already jumped out the window. There is no conceivable way to carry enough reaction mass along on a spaceship to reach a large fraction of light speed using rockets. Even photon rockets, unless you're cracking zero-point energies or something.

The Bussard ramship gets around this, but opens whole new cans of worms. I have only seen laser-driven sails for "slow" vehicles, and don't think relativistic pumped sails are in the picture. Anyway, that particular system screws up your "abandoned in space" plot. Needs self-contained ships.

And hey, your "entanglers" have Magic Drives. How plausible are they? ;)