If the Big Bang happens more than once and universal expansion/contraction is cyclical, than perhaps the cycle is infinite and therefore, the tachyons could continue to travel back in time. For us to detect such a (particle?) wouldn't some other source than the Big Bang be responsible for the tachyons as our timeline is the furthest point in the future for every nanosecond that passes.
Who knows, perhaps ours is not the only universe and tachyons are not native to ours. A Black Hole does not capture everything. Maybe tachyons exist and are uneffected by events such as the Big Bang.
Just some thoughts over my morning cup of java. Thanks for the thread, gave my mind a kickstart this morning.