I would caution applying our current understanding and limitations onto alien civilizations. I don't believe they will break the light barrier, but they may develop telescopes that can detect life from light-years away, and the stupendous travel times are possible with suspended animation or by stopping the aging process.

While we don't know everything, we do know what we don't know needs to be consistent with what we know. Relativity is well supported by experiments, so whatever this thing is we don't know will have all the things you don't like about relativity.

telestope limits exist in theory not just our manufacturing abilities.