Can't interstellar travel just be impossible?
Assuming there's no way to sidestep GR, the real problem is the human lifespan (and attention span.)
If our culture moved at 0.1% of the current rate and we lived a thousand times as long, a 1400 year round trip wouldn't be problematic.
It's possible to imagine low-energy lifeforms that move that slowly. But they wouldn't be looking for Earth-like planets to colonise - they'd be looking for much colder and more stable locations.
And we wouldn't be looking for the right spectroscopic signals to give them away, because we don't know what they are.
Also worth noting is that all deep space missions thus far have had to rely on nuclear power, usually using 238-Pu with a half life of less than 90 years. With such technology, a well-shielded, self-correcting computer system traveling at reasonable speeds and energies could not survive too long because it would simply run out of power. AFAIK, workarounds for this rely on exotic power sources and unproven physics--it's entirely possible that these don't pan out, and this provides our "Great Filter."
As far as onboard power sources go, fission seems perfectly cromulent. You just have to protect those radiators.
> Since the tether current is 1,333 amps, ne = 3 X 10‘‘ m-3 and the ship’s velocity is 900 km/sec, the effective electron-collector radius is approximately 3 13 km.
This appears to have a toroidal-field ramscoop as a prerequisite.
For thrustless turning, a 0.06 degree turn requires a tether 10^3 km long:
> To obtain a six-degree trajectory modification during a 1,400-year journey with the tether current assumed, the tether length must be increased by a factor of lOOX to equal l0^5 km. This would increase tether mass to 2.7 X lo5 kg.
And this is using a reference ship many scientists are skeptical about:
> ...it is assumed here that the primary propulsion for these ships is the ultra-thin, space manufactured solar sail unfurled as close to the Sun as possible at the perihelion of a parabolic or hyperbolic solar orbit. After acceleration to interstellar cruise velocity, it is also assumed that sail and cables are wound around the habitat section to provide extra cosmic ray shielding. The sail is unfurled again for deceleration at the destination star.... since the baseline sailcraft for this analysis is somewhat faster, either more advanced sail/cable materials are required or the pre-perihelion orbit is hyperbolic.
I'd definitely categorize that under "experimental power sources and unproven physics." Perhaps you are thinking of a different article?
There are about 10 stars we know about within 11-ly of earth. A serious attempt to reach one would involve doing slingshots around many bodies in the solar system, probably culminating with a dive to the Sun in order where the major rockets would be fired. (The Oberth effect says you get the most ∆v boost at the point closest to the orbiting body. You cannot logically use the Sun as a passive slingshot because you are trying to leave the solar system.) Getting the speed to 1% of c this way looks entirely reasonable, which gives about a century of travel time.
It would be very expensive, but in a few more centuries society will be a lot richer. This is also something that would only occur after significant colonization within the solar system, and mapping of distant star systems to find good candidate systems.
What if we (and every other intelligent life) just level off when we start reaching the limits of physics and the available resources within our own solar system?
Therefore inter-species conflicts are resolved by mass/energy available. Any civilization that doesn't expand to interstellar levels of power is subject to the whims of those that do. If you can expand, you must.