Make the model scale to be 10000000 (10 million). The sun is a chunky 139 meters in diameter. Earth is 15 km (9 miles) away. Pluto is 587 km (365 miles) away. The speed of light is 107 kph (67 mph).
Alpha Centauri is 4.1 million km (2.5 million miles) away... that is 10 times the earth moon distance.
Another comparison... Voyager 1 is moving at 30 light minutes per year. (Andromeda galaxy is approaching the Milky Way at 3.2 light hours per year)
75k years in geological timescales is nothing.
If there are creatures who could live longer than that, perhaps by hibernating or just having really long lifetimes, space exploration is feasible with slow craft.
If you can make that kind of trip the question becomes why bother? You could have used the same technology (actually a much easier version of the tech since you will have access to external resources and don't need to attach enormous engines to get it moving and then stopping at the destination) to use the almost unlimited space in your home solar system instead.
Unless your sun is literally about to explode it is hard to make the argument for the incredibly difficult and long journey to a neighboring solar system.
This is also called "Everything we know about physics is so radically wrong that it shouldn't be possible for us to make the predictions we do"
Reactionless drives are not physical, or if they are physically possible, will have such unique quirks and constraints as to be meaningless outside of some insane laboratory setup.
For example, making very high weight new atoms that have never existed in the universe before is physically possible, but the realities of making those atoms and their nuclear instability means it doesn't matter even if a super heavy element has some crazy properties that we would like to exploit, because there will never be enough of that element to make anything out of. The "rules" of atoms should still work well above 180 protons, but other physics makes that meaningless.
Without reactionless drives, interstellar travel is so physically difficult to be essentially impossible, and no amount of engineering or cleverness can change that.